Toric orbifolds associated with partitioned weight polytopes in classical types
Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Horiguchi, Tatsuya [verfasserIn] Masuda, Mikiya [verfasserIn] Shareshian, John [verfasserIn] Song, Jongbaek [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2024 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
|---|
| Übergeordnetes Werk: |
Enthalten in: Selecta mathematica - Springer International Publishing, 1995, 30(2024), 5 vom: 27. Sept. |
|---|---|
| Übergeordnetes Werk: |
volume:30 ; year:2024 ; number:5 ; day:27 ; month:09 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00029-024-00977-9 |
|---|
| Katalog-ID: |
SPR05748757X |
|---|
| LEADER | 01000naa a22002652 4500 | ||
|---|---|---|---|
| 001 | SPR05748757X | ||
| 003 | DE-627 | ||
| 005 | 20240928072424.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 240928s2024 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s00029-024-00977-9 |2 doi | |
| 035 | |a (DE-627)SPR05748757X | ||
| 035 | |a (SPR)s00029-024-00977-9-e | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 510 |q VZ |
| 084 | |a 31.00 |2 bkl | ||
| 100 | 1 | |a Horiguchi, Tatsuya |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Toric orbifolds associated with partitioned weight polytopes in classical types |
| 264 | 1 | |c 2024 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. | ||
| 520 | |a Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of p. The representation of W on the rational cohomology ring $$H^*(X_\Phi )$$ of the toric variety $$X_\Phi $$ associated to (the normal fan to) $$P_W$$ has been studied by various authors. Let $$\{s_1,\ldots ,s_n\}$$ be a complete set of simple reflections in W. For $$K \subseteq [n]$$, let $$W_K$$ be the standard parabolic subgroup of W generated by $$\{s_k:k \in K\}$$. We show that the fixed subring $$H^*(X_\Phi )^{W_K}$$ is isomorphic to the cohomology ring of the toric variety $$X_\Phi (K)$$ associated to a polytope obtained by intersecting $$P_W$$ with half-spaces bounded by reflecting hyperplanes for the given generators of $$W_K$$. We also obtain explicit formulas for h-vectors of these polytopes. By a result of Balibanu–Crooks, the cohomology rings $$H^*(X_\Phi (K))$$ are isomorphic with cohomology rings of certain regular Hessenberg varieties. | ||
| 650 | 4 | |a Toric varieties |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Root systems |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Cohomology |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Permutohedra |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Weight polytopes |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Weyl groups |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Parabolic subgroups |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Hessenberg varieties |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Masuda, Mikiya |e verfasserin |4 aut | |
| 700 | 1 | |a Shareshian, John |e verfasserin |4 aut | |
| 700 | 1 | |a Song, Jongbaek |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Selecta mathematica |d Springer International Publishing, 1995 |g 30(2024), 5 vom: 27. Sept. |w (DE-627)254638821 |w (DE-600)1462998-7 |x 1420-9020 |7 nnns |
| 773 | 1 | 8 | |g volume:30 |g year:2024 |g number:5 |g day:27 |g month:09 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00029-024-00977-9 |m X:SPRINGER |x Resolving-System |z lizenzpflichtig |3 Volltext |
| 912 | |a SYSFLAG_0 | ||
| 912 | |a GBV_SPRINGER | ||
| 912 | |a SSG-OPC-MAT | ||
| 912 | |a GBV_ILN_11 | ||
| 912 | |a GBV_ILN_20 | ||
| 912 | |a GBV_ILN_22 | ||
| 912 | |a GBV_ILN_23 | ||
| 912 | |a GBV_ILN_24 | ||
| 912 | |a GBV_ILN_31 | ||
| 912 | |a GBV_ILN_32 | ||
| 912 | |a GBV_ILN_39 | ||
| 912 | |a GBV_ILN_40 | ||
| 912 | |a GBV_ILN_60 | ||
| 912 | |a GBV_ILN_62 | ||
| 912 | |a GBV_ILN_63 | ||
| 912 | |a GBV_ILN_69 | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_72 | ||
| 912 | |a GBV_ILN_73 | ||
| 912 | |a GBV_ILN_74 | ||
| 912 | |a GBV_ILN_90 | ||
| 912 | |a GBV_ILN_95 | ||
| 912 | |a GBV_ILN_100 | ||
| 912 | |a GBV_ILN_105 | ||
| 912 | |a GBV_ILN_110 | ||
| 912 | |a GBV_ILN_120 | ||
| 912 | |a GBV_ILN_138 | ||
| 912 | |a GBV_ILN_150 | ||
| 912 | |a GBV_ILN_151 | ||
| 912 | |a GBV_ILN_152 | ||
| 912 | |a GBV_ILN_161 | ||
| 912 | |a GBV_ILN_170 | ||
| 912 | |a GBV_ILN_171 | ||
| 912 | |a GBV_ILN_187 | ||
| 912 | |a GBV_ILN_213 | ||
| 912 | |a GBV_ILN_224 | ||
| 912 | |a GBV_ILN_230 | ||
| 912 | |a GBV_ILN_250 | ||
| 912 | |a GBV_ILN_267 | ||
| 912 | |a GBV_ILN_281 | ||
| 912 | |a GBV_ILN_285 | ||
| 912 | |a GBV_ILN_293 | ||
| 912 | |a GBV_ILN_370 | ||
| 912 | |a GBV_ILN_602 | ||
| 912 | |a GBV_ILN_636 | ||
| 912 | |a GBV_ILN_702 | ||
| 912 | |a GBV_ILN_2001 | ||
| 912 | |a GBV_ILN_2003 | ||
| 912 | |a GBV_ILN_2004 | ||
| 912 | |a GBV_ILN_2005 | ||
| 912 | |a GBV_ILN_2006 | ||
| 912 | |a GBV_ILN_2007 | ||
| 912 | |a GBV_ILN_2009 | ||
| 912 | |a GBV_ILN_2010 | ||
| 912 | |a GBV_ILN_2011 | ||
| 912 | |a GBV_ILN_2014 | ||
| 912 | |a GBV_ILN_2015 | ||
| 912 | |a GBV_ILN_2020 | ||
| 912 | |a GBV_ILN_2021 | ||
| 912 | |a GBV_ILN_2025 | ||
| 912 | |a GBV_ILN_2026 | ||
| 912 | |a GBV_ILN_2027 | ||
| 912 | |a GBV_ILN_2031 | ||
| 912 | |a GBV_ILN_2034 | ||
| 912 | |a GBV_ILN_2037 | ||
| 912 | |a GBV_ILN_2038 | ||
| 912 | |a GBV_ILN_2039 | ||
| 912 | |a GBV_ILN_2044 | ||
| 912 | |a GBV_ILN_2048 | ||
| 912 | |a GBV_ILN_2049 | ||
| 912 | |a GBV_ILN_2050 | ||
| 912 | |a GBV_ILN_2055 | ||
| 912 | |a GBV_ILN_2056 | ||
| 912 | |a GBV_ILN_2057 | ||
| 912 | |a GBV_ILN_2059 | ||
| 912 | |a GBV_ILN_2061 | ||
| 912 | |a GBV_ILN_2064 | ||
| 912 | |a GBV_ILN_2065 | ||
| 912 | |a GBV_ILN_2068 | ||
| 912 | |a GBV_ILN_2088 | ||
| 912 | |a GBV_ILN_2093 | ||
| 912 | |a GBV_ILN_2106 | ||
| 912 | |a GBV_ILN_2107 | ||
| 912 | |a GBV_ILN_2108 | ||
| 912 | |a GBV_ILN_2110 | ||
| 912 | |a GBV_ILN_2111 | ||
| 912 | |a GBV_ILN_2112 | ||
| 912 | |a GBV_ILN_2113 | ||
| 912 | |a GBV_ILN_2118 | ||
| 912 | |a GBV_ILN_2122 | ||
| 912 | |a GBV_ILN_2129 | ||
| 912 | |a GBV_ILN_2143 | ||
| 912 | |a GBV_ILN_2144 | ||
| 912 | |a GBV_ILN_2147 | ||
| 912 | |a GBV_ILN_2148 | ||
| 912 | |a GBV_ILN_2152 | ||
| 912 | |a GBV_ILN_2153 | ||
| 912 | |a GBV_ILN_2188 | ||
| 912 | |a GBV_ILN_2190 | ||
| 912 | |a GBV_ILN_2232 | ||
| 912 | |a GBV_ILN_2336 | ||
| 912 | |a GBV_ILN_2446 | ||
| 912 | |a GBV_ILN_2470 | ||
| 912 | |a GBV_ILN_2472 | ||
| 912 | |a GBV_ILN_2507 | ||
| 912 | |a GBV_ILN_2522 | ||
| 912 | |a GBV_ILN_2548 | ||
| 912 | |a GBV_ILN_2574 | ||
| 912 | |a GBV_ILN_4035 | ||
| 912 | |a GBV_ILN_4037 | ||
| 912 | |a GBV_ILN_4046 | ||
| 912 | |a GBV_ILN_4112 | ||
| 912 | |a GBV_ILN_4125 | ||
| 912 | |a GBV_ILN_4126 | ||
| 912 | |a GBV_ILN_4242 | ||
| 912 | |a GBV_ILN_4246 | ||
| 912 | |a GBV_ILN_4249 | ||
| 912 | |a GBV_ILN_4251 | ||
| 912 | |a GBV_ILN_4305 | ||
| 912 | |a GBV_ILN_4306 | ||
| 912 | |a GBV_ILN_4307 | ||
| 912 | |a GBV_ILN_4313 | ||
| 912 | |a GBV_ILN_4322 | ||
| 912 | |a GBV_ILN_4323 | ||
| 912 | |a GBV_ILN_4324 | ||
| 912 | |a GBV_ILN_4325 | ||
| 912 | |a GBV_ILN_4326 | ||
| 912 | |a GBV_ILN_4328 | ||
| 912 | |a GBV_ILN_4333 | ||
| 912 | |a GBV_ILN_4334 | ||
| 912 | |a GBV_ILN_4335 | ||
| 912 | |a GBV_ILN_4336 | ||
| 912 | |a GBV_ILN_4338 | ||
| 912 | |a GBV_ILN_4393 | ||
| 912 | |a GBV_ILN_4700 | ||
| 936 | b | k | |a 31.00 |q VZ |
| 951 | |a AR | ||
| 952 | |d 30 |j 2024 |e 5 |b 27 |c 09 | ||
| author_variant |
t h th m m mm j s js j s js |
|---|---|
| matchkey_str |
article:14209020:2024----::oiobflssoitdihattoewihplt |
| hierarchy_sort_str |
2024 |
| bklnumber |
31.00 |
| publishDate |
2024 |
| allfields |
10.1007/s00029-024-00977-9 doi (DE-627)SPR05748757X (SPR)s00029-024-00977-9-e DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl Horiguchi, Tatsuya verfasserin aut Toric orbifolds associated with partitioned weight polytopes in classical types 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of p. The representation of W on the rational cohomology ring $$H^*(X_\Phi )$$ of the toric variety $$X_\Phi $$ associated to (the normal fan to) $$P_W$$ has been studied by various authors. Let $$\{s_1,\ldots ,s_n\}$$ be a complete set of simple reflections in W. For $$K \subseteq [n]$$, let $$W_K$$ be the standard parabolic subgroup of W generated by $$\{s_k:k \in K\}$$. We show that the fixed subring $$H^*(X_\Phi )^{W_K}$$ is isomorphic to the cohomology ring of the toric variety $$X_\Phi (K)$$ associated to a polytope obtained by intersecting $$P_W$$ with half-spaces bounded by reflecting hyperplanes for the given generators of $$W_K$$. We also obtain explicit formulas for h-vectors of these polytopes. By a result of Balibanu–Crooks, the cohomology rings $$H^*(X_\Phi (K))$$ are isomorphic with cohomology rings of certain regular Hessenberg varieties. Toric varieties (dpeaa)DE-He213 Root systems (dpeaa)DE-He213 Cohomology (dpeaa)DE-He213 Permutohedra (dpeaa)DE-He213 Weight polytopes (dpeaa)DE-He213 Weyl groups (dpeaa)DE-He213 Parabolic subgroups (dpeaa)DE-He213 Hessenberg varieties (dpeaa)DE-He213 Masuda, Mikiya verfasserin aut Shareshian, John verfasserin aut Song, Jongbaek verfasserin aut Enthalten in Selecta mathematica Springer International Publishing, 1995 30(2024), 5 vom: 27. Sept. (DE-627)254638821 (DE-600)1462998-7 1420-9020 nnns volume:30 year:2024 number:5 day:27 month:09 https://dx.doi.org/10.1007/s00029-024-00977-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 30 2024 5 27 09 |
| spelling |
10.1007/s00029-024-00977-9 doi (DE-627)SPR05748757X (SPR)s00029-024-00977-9-e DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl Horiguchi, Tatsuya verfasserin aut Toric orbifolds associated with partitioned weight polytopes in classical types 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of p. The representation of W on the rational cohomology ring $$H^*(X_\Phi )$$ of the toric variety $$X_\Phi $$ associated to (the normal fan to) $$P_W$$ has been studied by various authors. Let $$\{s_1,\ldots ,s_n\}$$ be a complete set of simple reflections in W. For $$K \subseteq [n]$$, let $$W_K$$ be the standard parabolic subgroup of W generated by $$\{s_k:k \in K\}$$. We show that the fixed subring $$H^*(X_\Phi )^{W_K}$$ is isomorphic to the cohomology ring of the toric variety $$X_\Phi (K)$$ associated to a polytope obtained by intersecting $$P_W$$ with half-spaces bounded by reflecting hyperplanes for the given generators of $$W_K$$. We also obtain explicit formulas for h-vectors of these polytopes. By a result of Balibanu–Crooks, the cohomology rings $$H^*(X_\Phi (K))$$ are isomorphic with cohomology rings of certain regular Hessenberg varieties. Toric varieties (dpeaa)DE-He213 Root systems (dpeaa)DE-He213 Cohomology (dpeaa)DE-He213 Permutohedra (dpeaa)DE-He213 Weight polytopes (dpeaa)DE-He213 Weyl groups (dpeaa)DE-He213 Parabolic subgroups (dpeaa)DE-He213 Hessenberg varieties (dpeaa)DE-He213 Masuda, Mikiya verfasserin aut Shareshian, John verfasserin aut Song, Jongbaek verfasserin aut Enthalten in Selecta mathematica Springer International Publishing, 1995 30(2024), 5 vom: 27. Sept. (DE-627)254638821 (DE-600)1462998-7 1420-9020 nnns volume:30 year:2024 number:5 day:27 month:09 https://dx.doi.org/10.1007/s00029-024-00977-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 30 2024 5 27 09 |
| allfields_unstemmed |
10.1007/s00029-024-00977-9 doi (DE-627)SPR05748757X (SPR)s00029-024-00977-9-e DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl Horiguchi, Tatsuya verfasserin aut Toric orbifolds associated with partitioned weight polytopes in classical types 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of p. The representation of W on the rational cohomology ring $$H^*(X_\Phi )$$ of the toric variety $$X_\Phi $$ associated to (the normal fan to) $$P_W$$ has been studied by various authors. Let $$\{s_1,\ldots ,s_n\}$$ be a complete set of simple reflections in W. For $$K \subseteq [n]$$, let $$W_K$$ be the standard parabolic subgroup of W generated by $$\{s_k:k \in K\}$$. We show that the fixed subring $$H^*(X_\Phi )^{W_K}$$ is isomorphic to the cohomology ring of the toric variety $$X_\Phi (K)$$ associated to a polytope obtained by intersecting $$P_W$$ with half-spaces bounded by reflecting hyperplanes for the given generators of $$W_K$$. We also obtain explicit formulas for h-vectors of these polytopes. By a result of Balibanu–Crooks, the cohomology rings $$H^*(X_\Phi (K))$$ are isomorphic with cohomology rings of certain regular Hessenberg varieties. Toric varieties (dpeaa)DE-He213 Root systems (dpeaa)DE-He213 Cohomology (dpeaa)DE-He213 Permutohedra (dpeaa)DE-He213 Weight polytopes (dpeaa)DE-He213 Weyl groups (dpeaa)DE-He213 Parabolic subgroups (dpeaa)DE-He213 Hessenberg varieties (dpeaa)DE-He213 Masuda, Mikiya verfasserin aut Shareshian, John verfasserin aut Song, Jongbaek verfasserin aut Enthalten in Selecta mathematica Springer International Publishing, 1995 30(2024), 5 vom: 27. Sept. (DE-627)254638821 (DE-600)1462998-7 1420-9020 nnns volume:30 year:2024 number:5 day:27 month:09 https://dx.doi.org/10.1007/s00029-024-00977-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 30 2024 5 27 09 |
| allfieldsGer |
10.1007/s00029-024-00977-9 doi (DE-627)SPR05748757X (SPR)s00029-024-00977-9-e DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl Horiguchi, Tatsuya verfasserin aut Toric orbifolds associated with partitioned weight polytopes in classical types 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of p. The representation of W on the rational cohomology ring $$H^*(X_\Phi )$$ of the toric variety $$X_\Phi $$ associated to (the normal fan to) $$P_W$$ has been studied by various authors. Let $$\{s_1,\ldots ,s_n\}$$ be a complete set of simple reflections in W. For $$K \subseteq [n]$$, let $$W_K$$ be the standard parabolic subgroup of W generated by $$\{s_k:k \in K\}$$. We show that the fixed subring $$H^*(X_\Phi )^{W_K}$$ is isomorphic to the cohomology ring of the toric variety $$X_\Phi (K)$$ associated to a polytope obtained by intersecting $$P_W$$ with half-spaces bounded by reflecting hyperplanes for the given generators of $$W_K$$. We also obtain explicit formulas for h-vectors of these polytopes. By a result of Balibanu–Crooks, the cohomology rings $$H^*(X_\Phi (K))$$ are isomorphic with cohomology rings of certain regular Hessenberg varieties. Toric varieties (dpeaa)DE-He213 Root systems (dpeaa)DE-He213 Cohomology (dpeaa)DE-He213 Permutohedra (dpeaa)DE-He213 Weight polytopes (dpeaa)DE-He213 Weyl groups (dpeaa)DE-He213 Parabolic subgroups (dpeaa)DE-He213 Hessenberg varieties (dpeaa)DE-He213 Masuda, Mikiya verfasserin aut Shareshian, John verfasserin aut Song, Jongbaek verfasserin aut Enthalten in Selecta mathematica Springer International Publishing, 1995 30(2024), 5 vom: 27. Sept. (DE-627)254638821 (DE-600)1462998-7 1420-9020 nnns volume:30 year:2024 number:5 day:27 month:09 https://dx.doi.org/10.1007/s00029-024-00977-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 30 2024 5 27 09 |
| allfieldsSound |
10.1007/s00029-024-00977-9 doi (DE-627)SPR05748757X (SPR)s00029-024-00977-9-e DE-627 ger DE-627 rakwb eng 510 VZ 31.00 bkl Horiguchi, Tatsuya verfasserin aut Toric orbifolds associated with partitioned weight polytopes in classical types 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of p. The representation of W on the rational cohomology ring $$H^*(X_\Phi )$$ of the toric variety $$X_\Phi $$ associated to (the normal fan to) $$P_W$$ has been studied by various authors. Let $$\{s_1,\ldots ,s_n\}$$ be a complete set of simple reflections in W. For $$K \subseteq [n]$$, let $$W_K$$ be the standard parabolic subgroup of W generated by $$\{s_k:k \in K\}$$. We show that the fixed subring $$H^*(X_\Phi )^{W_K}$$ is isomorphic to the cohomology ring of the toric variety $$X_\Phi (K)$$ associated to a polytope obtained by intersecting $$P_W$$ with half-spaces bounded by reflecting hyperplanes for the given generators of $$W_K$$. We also obtain explicit formulas for h-vectors of these polytopes. By a result of Balibanu–Crooks, the cohomology rings $$H^*(X_\Phi (K))$$ are isomorphic with cohomology rings of certain regular Hessenberg varieties. Toric varieties (dpeaa)DE-He213 Root systems (dpeaa)DE-He213 Cohomology (dpeaa)DE-He213 Permutohedra (dpeaa)DE-He213 Weight polytopes (dpeaa)DE-He213 Weyl groups (dpeaa)DE-He213 Parabolic subgroups (dpeaa)DE-He213 Hessenberg varieties (dpeaa)DE-He213 Masuda, Mikiya verfasserin aut Shareshian, John verfasserin aut Song, Jongbaek verfasserin aut Enthalten in Selecta mathematica Springer International Publishing, 1995 30(2024), 5 vom: 27. Sept. (DE-627)254638821 (DE-600)1462998-7 1420-9020 nnns volume:30 year:2024 number:5 day:27 month:09 https://dx.doi.org/10.1007/s00029-024-00977-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 30 2024 5 27 09 |
| language |
English |
| source |
Enthalten in Selecta mathematica 30(2024), 5 vom: 27. Sept. volume:30 year:2024 number:5 day:27 month:09 |
| sourceStr |
Enthalten in Selecta mathematica 30(2024), 5 vom: 27. Sept. volume:30 year:2024 number:5 day:27 month:09 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Toric varieties Root systems Cohomology Permutohedra Weight polytopes Weyl groups Parabolic subgroups Hessenberg varieties |
| dewey-raw |
510 |
| isfreeaccess_bool |
false |
| container_title |
Selecta mathematica |
| authorswithroles_txt_mv |
Horiguchi, Tatsuya @@aut@@ Masuda, Mikiya @@aut@@ Shareshian, John @@aut@@ Song, Jongbaek @@aut@@ |
| publishDateDaySort_date |
2024-09-27T00:00:00Z |
| hierarchy_top_id |
254638821 |
| dewey-sort |
3510 |
| id |
SPR05748757X |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR05748757X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240928072424.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">240928s2024 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00029-024-00977-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR05748757X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00029-024-00977-9-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Horiguchi, Tatsuya</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Toric orbifolds associated with partitioned weight polytopes in classical types</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2024</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of p. The representation of W on the rational cohomology ring $$H^*(X_\Phi )$$ of the toric variety $$X_\Phi $$ associated to (the normal fan to) $$P_W$$ has been studied by various authors. Let $$\{s_1,\ldots ,s_n\}$$ be a complete set of simple reflections in W. For $$K \subseteq [n]$$, let $$W_K$$ be the standard parabolic subgroup of W generated by $$\{s_k:k \in K\}$$. We show that the fixed subring $$H^*(X_\Phi )^{W_K}$$ is isomorphic to the cohomology ring of the toric variety $$X_\Phi (K)$$ associated to a polytope obtained by intersecting $$P_W$$ with half-spaces bounded by reflecting hyperplanes for the given generators of $$W_K$$. We also obtain explicit formulas for h-vectors of these polytopes. By a result of Balibanu–Crooks, the cohomology rings $$H^*(X_\Phi (K))$$ are isomorphic with cohomology rings of certain regular Hessenberg varieties.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Toric varieties</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Root systems</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cohomology</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Permutohedra</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Weight polytopes</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Weyl groups</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Parabolic subgroups</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hessenberg varieties</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Masuda, Mikiya</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Shareshian, John</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Song, Jongbaek</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Selecta mathematica</subfield><subfield code="d">Springer International Publishing, 1995</subfield><subfield code="g">30(2024), 5 vom: 27. Sept.</subfield><subfield code="w">(DE-627)254638821</subfield><subfield code="w">(DE-600)1462998-7</subfield><subfield code="x">1420-9020</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:30</subfield><subfield code="g">year:2024</subfield><subfield code="g">number:5</subfield><subfield code="g">day:27</subfield><subfield code="g">month:09</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00029-024-00977-9</subfield><subfield code="m">X:SPRINGER</subfield><subfield code="x">Resolving-System</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_0</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_72</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_120</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_138</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_171</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_250</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_267</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_281</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_636</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2001</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2007</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2009</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2010</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2026</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2031</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2038</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2039</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2055</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2056</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2057</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2065</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2068</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2093</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2106</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2107</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2108</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2113</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2118</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2144</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2147</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2148</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2188</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2232</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2446</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2470</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2472</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2522</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2548</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2574</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4046</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4246</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4328</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">31.00</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">30</subfield><subfield code="j">2024</subfield><subfield code="e">5</subfield><subfield code="b">27</subfield><subfield code="c">09</subfield></datafield></record></collection>
|
| author |
Horiguchi, Tatsuya |
| spellingShingle |
Horiguchi, Tatsuya ddc 510 bkl 31.00 misc Toric varieties misc Root systems misc Cohomology misc Permutohedra misc Weight polytopes misc Weyl groups misc Parabolic subgroups misc Hessenberg varieties Toric orbifolds associated with partitioned weight polytopes in classical types |
| authorStr |
Horiguchi, Tatsuya |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)254638821 |
| format |
electronic Article |
| dewey-ones |
510 - Mathematics |
| delete_txt_mv |
keep |
| author_role |
aut aut aut aut |
| collection |
springer |
| remote_str |
true |
| illustrated |
Not Illustrated |
| issn |
1420-9020 |
| topic_title |
510 VZ 31.00 bkl Toric orbifolds associated with partitioned weight polytopes in classical types Toric varieties (dpeaa)DE-He213 Root systems (dpeaa)DE-He213 Cohomology (dpeaa)DE-He213 Permutohedra (dpeaa)DE-He213 Weight polytopes (dpeaa)DE-He213 Weyl groups (dpeaa)DE-He213 Parabolic subgroups (dpeaa)DE-He213 Hessenberg varieties (dpeaa)DE-He213 |
| topic |
ddc 510 bkl 31.00 misc Toric varieties misc Root systems misc Cohomology misc Permutohedra misc Weight polytopes misc Weyl groups misc Parabolic subgroups misc Hessenberg varieties |
| topic_unstemmed |
ddc 510 bkl 31.00 misc Toric varieties misc Root systems misc Cohomology misc Permutohedra misc Weight polytopes misc Weyl groups misc Parabolic subgroups misc Hessenberg varieties |
| topic_browse |
ddc 510 bkl 31.00 misc Toric varieties misc Root systems misc Cohomology misc Permutohedra misc Weight polytopes misc Weyl groups misc Parabolic subgroups misc Hessenberg varieties |
| format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
cr |
| hierarchy_parent_title |
Selecta mathematica |
| hierarchy_parent_id |
254638821 |
| dewey-tens |
510 - Mathematics |
| hierarchy_top_title |
Selecta mathematica |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)254638821 (DE-600)1462998-7 |
| title |
Toric orbifolds associated with partitioned weight polytopes in classical types |
| ctrlnum |
(DE-627)SPR05748757X (SPR)s00029-024-00977-9-e |
| title_full |
Toric orbifolds associated with partitioned weight polytopes in classical types |
| author_sort |
Horiguchi, Tatsuya |
| journal |
Selecta mathematica |
| journalStr |
Selecta mathematica |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2024 |
| contenttype_str_mv |
txt |
| author_browse |
Horiguchi, Tatsuya Masuda, Mikiya Shareshian, John Song, Jongbaek |
| container_volume |
30 |
| class |
510 VZ 31.00 bkl |
| format_se |
Elektronische Aufsätze |
| author-letter |
Horiguchi, Tatsuya |
| doi_str_mv |
10.1007/s00029-024-00977-9 |
| dewey-full |
510 |
| author2-role |
verfasserin |
| title_sort |
toric orbifolds associated with partitioned weight polytopes in classical types |
| title_auth |
Toric orbifolds associated with partitioned weight polytopes in classical types |
| abstract |
Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of p. The representation of W on the rational cohomology ring $$H^*(X_\Phi )$$ of the toric variety $$X_\Phi $$ associated to (the normal fan to) $$P_W$$ has been studied by various authors. Let $$\{s_1,\ldots ,s_n\}$$ be a complete set of simple reflections in W. For $$K \subseteq [n]$$, let $$W_K$$ be the standard parabolic subgroup of W generated by $$\{s_k:k \in K\}$$. We show that the fixed subring $$H^*(X_\Phi )^{W_K}$$ is isomorphic to the cohomology ring of the toric variety $$X_\Phi (K)$$ associated to a polytope obtained by intersecting $$P_W$$ with half-spaces bounded by reflecting hyperplanes for the given generators of $$W_K$$. We also obtain explicit formulas for h-vectors of these polytopes. By a result of Balibanu–Crooks, the cohomology rings $$H^*(X_\Phi (K))$$ are isomorphic with cohomology rings of certain regular Hessenberg varieties. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of p. The representation of W on the rational cohomology ring $$H^*(X_\Phi )$$ of the toric variety $$X_\Phi $$ associated to (the normal fan to) $$P_W$$ has been studied by various authors. Let $$\{s_1,\ldots ,s_n\}$$ be a complete set of simple reflections in W. For $$K \subseteq [n]$$, let $$W_K$$ be the standard parabolic subgroup of W generated by $$\{s_k:k \in K\}$$. We show that the fixed subring $$H^*(X_\Phi )^{W_K}$$ is isomorphic to the cohomology ring of the toric variety $$X_\Phi (K)$$ associated to a polytope obtained by intersecting $$P_W$$ with half-spaces bounded by reflecting hyperplanes for the given generators of $$W_K$$. We also obtain explicit formulas for h-vectors of these polytopes. By a result of Balibanu–Crooks, the cohomology rings $$H^*(X_\Phi (K))$$ are isomorphic with cohomology rings of certain regular Hessenberg varieties. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of p. The representation of W on the rational cohomology ring $$H^*(X_\Phi )$$ of the toric variety $$X_\Phi $$ associated to (the normal fan to) $$P_W$$ has been studied by various authors. Let $$\{s_1,\ldots ,s_n\}$$ be a complete set of simple reflections in W. For $$K \subseteq [n]$$, let $$W_K$$ be the standard parabolic subgroup of W generated by $$\{s_k:k \in K\}$$. We show that the fixed subring $$H^*(X_\Phi )^{W_K}$$ is isomorphic to the cohomology ring of the toric variety $$X_\Phi (K)$$ associated to a polytope obtained by intersecting $$P_W$$ with half-spaces bounded by reflecting hyperplanes for the given generators of $$W_K$$. We also obtain explicit formulas for h-vectors of these polytopes. By a result of Balibanu–Crooks, the cohomology rings $$H^*(X_\Phi (K))$$ are isomorphic with cohomology rings of certain regular Hessenberg varieties. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| collection_details |
SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 |
| container_issue |
5 |
| title_short |
Toric orbifolds associated with partitioned weight polytopes in classical types |
| url |
https://dx.doi.org/10.1007/s00029-024-00977-9 |
| remote_bool |
true |
| author2 |
Masuda, Mikiya Shareshian, John Song, Jongbaek |
| author2Str |
Masuda, Mikiya Shareshian, John Song, Jongbaek |
| ppnlink |
254638821 |
| mediatype_str_mv |
c |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s00029-024-00977-9 |
| up_date |
2024-09-28T05:27:04.624Z |
| _version_ |
1811416324105043968 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR05748757X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240928072424.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">240928s2024 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00029-024-00977-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR05748757X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00029-024-00977-9-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Horiguchi, Tatsuya</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Toric orbifolds associated with partitioned weight polytopes in classical types</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2024</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Given a root system $$\Phi $$ of type $$A_n$$, $$B_n$$, $$C_n$$, or $$D_n$$ in Euclidean space E, let W be the associated Weyl group. For a point $$p \in E$$ not orthogonal to any of the roots in $$\Phi $$, we consider the W-permutohedron $$P_W$$, which is the convex hull of the W-orbit of p. The representation of W on the rational cohomology ring $$H^*(X_\Phi )$$ of the toric variety $$X_\Phi $$ associated to (the normal fan to) $$P_W$$ has been studied by various authors. Let $$\{s_1,\ldots ,s_n\}$$ be a complete set of simple reflections in W. For $$K \subseteq [n]$$, let $$W_K$$ be the standard parabolic subgroup of W generated by $$\{s_k:k \in K\}$$. We show that the fixed subring $$H^*(X_\Phi )^{W_K}$$ is isomorphic to the cohomology ring of the toric variety $$X_\Phi (K)$$ associated to a polytope obtained by intersecting $$P_W$$ with half-spaces bounded by reflecting hyperplanes for the given generators of $$W_K$$. We also obtain explicit formulas for h-vectors of these polytopes. By a result of Balibanu–Crooks, the cohomology rings $$H^*(X_\Phi (K))$$ are isomorphic with cohomology rings of certain regular Hessenberg varieties.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Toric varieties</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Root systems</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cohomology</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Permutohedra</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Weight polytopes</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Weyl groups</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Parabolic subgroups</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hessenberg varieties</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Masuda, Mikiya</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Shareshian, John</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Song, Jongbaek</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Selecta mathematica</subfield><subfield code="d">Springer International Publishing, 1995</subfield><subfield code="g">30(2024), 5 vom: 27. Sept.</subfield><subfield code="w">(DE-627)254638821</subfield><subfield code="w">(DE-600)1462998-7</subfield><subfield code="x">1420-9020</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:30</subfield><subfield code="g">year:2024</subfield><subfield code="g">number:5</subfield><subfield code="g">day:27</subfield><subfield code="g">month:09</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00029-024-00977-9</subfield><subfield code="m">X:SPRINGER</subfield><subfield code="x">Resolving-System</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_0</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_72</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_120</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_138</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_171</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_250</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_267</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_281</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_636</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2001</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2007</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2009</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2010</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2026</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2031</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2038</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2039</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2055</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2056</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2057</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2065</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2068</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2093</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2106</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2107</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2108</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2113</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2118</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2144</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2147</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2148</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2188</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2232</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2446</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2470</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2472</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2522</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2548</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2574</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4046</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4246</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4328</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">31.00</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">30</subfield><subfield code="j">2024</subfield><subfield code="e">5</subfield><subfield code="b">27</subfield><subfield code="c">09</subfield></datafield></record></collection>
|
| score |
7.4016123 |