Positive expressions for skew divided difference operators
Abstract For permutations %$v,w \in \mathfrak S_n%$, Macdonald defines the skew divided difference operators %$\partial _{w/v}%$ as the unique linear operators satisfying %$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ%$ for all polynomials %$P%$ and %$Q%$. We prove that %$\partia...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Liu, Ricky Ini [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of algebraic combinatorics - Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992, 42(2015), 3 vom: 15. Mai, Seite 861-874 |
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| Übergeordnetes Werk: |
volume:42 ; year:2015 ; number:3 ; day:15 ; month:05 ; pages:861-874 |
| Links: |
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| DOI / URN: |
10.1007/s10801-015-0606-1 |
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| Katalog-ID: |
SPR01332554X |
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| 520 | |a Abstract For permutations %$v,w \in \mathfrak S_n%$, Macdonald defines the skew divided difference operators %$\partial _{w/v}%$ as the unique linear operators satisfying %$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ%$ for all polynomials %$P%$ and %$Q%$. We prove that %$\partial _{w/v}%$ has a positive expression in terms of divided difference operators %$\partial _{ij}%$ for %$i<j%$. In fact, we prove that the analogous result holds in the Fomin–Kirillov algebra %${\mathcal {E}}_n%$, which settles a conjecture of Kirillov. | ||
| 650 | 4 | |a Skew divided difference operator |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Fomin–Kirillov algebra |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Braided Hopf algebra |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Bruhat order |7 (dpeaa)DE-He213 | |
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10.1007/s10801-015-0606-1 doi (DE-627)SPR01332554X (SPR)s10801-015-0606-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.12 bkl 31.20 bkl Liu, Ricky Ini verfasserin aut Positive expressions for skew divided difference operators 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract For permutations %$v,w \in \mathfrak S_n%$, Macdonald defines the skew divided difference operators %$\partial _{w/v}%$ as the unique linear operators satisfying %$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ%$ for all polynomials %$P%$ and %$Q%$. We prove that %$\partial _{w/v}%$ has a positive expression in terms of divided difference operators %$\partial _{ij}%$ for %$i<j%$. In fact, we prove that the analogous result holds in the Fomin–Kirillov algebra %${\mathcal {E}}_n%$, which settles a conjecture of Kirillov. Skew divided difference operator (dpeaa)DE-He213 Fomin–Kirillov algebra (dpeaa)DE-He213 Braided Hopf algebra (dpeaa)DE-He213 Bruhat order (dpeaa)DE-He213 Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 42(2015), 3 vom: 15. Mai, Seite 861-874 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:42 year:2015 number:3 day:15 month:05 pages:861-874 https://dx.doi.org/10.1007/s10801-015-0606-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_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_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 31.12 ASE 31.20 ASE AR 42 2015 3 15 05 861-874 |
| spelling |
10.1007/s10801-015-0606-1 doi (DE-627)SPR01332554X (SPR)s10801-015-0606-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.12 bkl 31.20 bkl Liu, Ricky Ini verfasserin aut Positive expressions for skew divided difference operators 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract For permutations %$v,w \in \mathfrak S_n%$, Macdonald defines the skew divided difference operators %$\partial _{w/v}%$ as the unique linear operators satisfying %$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ%$ for all polynomials %$P%$ and %$Q%$. We prove that %$\partial _{w/v}%$ has a positive expression in terms of divided difference operators %$\partial _{ij}%$ for %$i<j%$. In fact, we prove that the analogous result holds in the Fomin–Kirillov algebra %${\mathcal {E}}_n%$, which settles a conjecture of Kirillov. Skew divided difference operator (dpeaa)DE-He213 Fomin–Kirillov algebra (dpeaa)DE-He213 Braided Hopf algebra (dpeaa)DE-He213 Bruhat order (dpeaa)DE-He213 Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 42(2015), 3 vom: 15. Mai, Seite 861-874 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:42 year:2015 number:3 day:15 month:05 pages:861-874 https://dx.doi.org/10.1007/s10801-015-0606-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_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_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 31.12 ASE 31.20 ASE AR 42 2015 3 15 05 861-874 |
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10.1007/s10801-015-0606-1 doi (DE-627)SPR01332554X (SPR)s10801-015-0606-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.12 bkl 31.20 bkl Liu, Ricky Ini verfasserin aut Positive expressions for skew divided difference operators 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract For permutations %$v,w \in \mathfrak S_n%$, Macdonald defines the skew divided difference operators %$\partial _{w/v}%$ as the unique linear operators satisfying %$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ%$ for all polynomials %$P%$ and %$Q%$. We prove that %$\partial _{w/v}%$ has a positive expression in terms of divided difference operators %$\partial _{ij}%$ for %$i<j%$. In fact, we prove that the analogous result holds in the Fomin–Kirillov algebra %${\mathcal {E}}_n%$, which settles a conjecture of Kirillov. Skew divided difference operator (dpeaa)DE-He213 Fomin–Kirillov algebra (dpeaa)DE-He213 Braided Hopf algebra (dpeaa)DE-He213 Bruhat order (dpeaa)DE-He213 Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 42(2015), 3 vom: 15. Mai, Seite 861-874 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:42 year:2015 number:3 day:15 month:05 pages:861-874 https://dx.doi.org/10.1007/s10801-015-0606-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_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_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 31.12 ASE 31.20 ASE AR 42 2015 3 15 05 861-874 |
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10.1007/s10801-015-0606-1 doi (DE-627)SPR01332554X (SPR)s10801-015-0606-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.12 bkl 31.20 bkl Liu, Ricky Ini verfasserin aut Positive expressions for skew divided difference operators 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract For permutations %$v,w \in \mathfrak S_n%$, Macdonald defines the skew divided difference operators %$\partial _{w/v}%$ as the unique linear operators satisfying %$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ%$ for all polynomials %$P%$ and %$Q%$. We prove that %$\partial _{w/v}%$ has a positive expression in terms of divided difference operators %$\partial _{ij}%$ for %$i<j%$. In fact, we prove that the analogous result holds in the Fomin–Kirillov algebra %${\mathcal {E}}_n%$, which settles a conjecture of Kirillov. Skew divided difference operator (dpeaa)DE-He213 Fomin–Kirillov algebra (dpeaa)DE-He213 Braided Hopf algebra (dpeaa)DE-He213 Bruhat order (dpeaa)DE-He213 Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 42(2015), 3 vom: 15. Mai, Seite 861-874 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:42 year:2015 number:3 day:15 month:05 pages:861-874 https://dx.doi.org/10.1007/s10801-015-0606-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_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_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 31.12 ASE 31.20 ASE AR 42 2015 3 15 05 861-874 |
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10.1007/s10801-015-0606-1 doi (DE-627)SPR01332554X (SPR)s10801-015-0606-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.12 bkl 31.20 bkl Liu, Ricky Ini verfasserin aut Positive expressions for skew divided difference operators 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract For permutations %$v,w \in \mathfrak S_n%$, Macdonald defines the skew divided difference operators %$\partial _{w/v}%$ as the unique linear operators satisfying %$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ%$ for all polynomials %$P%$ and %$Q%$. We prove that %$\partial _{w/v}%$ has a positive expression in terms of divided difference operators %$\partial _{ij}%$ for %$i<j%$. In fact, we prove that the analogous result holds in the Fomin–Kirillov algebra %${\mathcal {E}}_n%$, which settles a conjecture of Kirillov. Skew divided difference operator (dpeaa)DE-He213 Fomin–Kirillov algebra (dpeaa)DE-He213 Braided Hopf algebra (dpeaa)DE-He213 Bruhat order (dpeaa)DE-He213 Enthalten in Journal of algebraic combinatorics Dordrecht [u.a.] : Springer Science + Business Media B.V., 1992 42(2015), 3 vom: 15. Mai, Seite 861-874 (DE-627)271180722 (DE-600)1479499-8 1572-9192 nnns volume:42 year:2015 number:3 day:15 month:05 pages:861-874 https://dx.doi.org/10.1007/s10801-015-0606-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_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_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_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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 31.12 ASE 31.20 ASE AR 42 2015 3 15 05 861-874 |
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Enthalten in Journal of algebraic combinatorics 42(2015), 3 vom: 15. Mai, Seite 861-874 volume:42 year:2015 number:3 day:15 month:05 pages:861-874 |
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Enthalten in Journal of algebraic combinatorics 42(2015), 3 vom: 15. Mai, Seite 861-874 volume:42 year:2015 number:3 day:15 month:05 pages:861-874 |
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Liu, Ricky Ini @@aut@@ |
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| author |
Liu, Ricky Ini |
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Liu, Ricky Ini ddc 510 bkl 31.12 bkl 31.20 misc Skew divided difference operator misc Fomin–Kirillov algebra misc Braided Hopf algebra misc Bruhat order Positive expressions for skew divided difference operators |
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510 ASE 31.12 bkl 31.20 bkl Positive expressions for skew divided difference operators Skew divided difference operator (dpeaa)DE-He213 Fomin–Kirillov algebra (dpeaa)DE-He213 Braided Hopf algebra (dpeaa)DE-He213 Bruhat order (dpeaa)DE-He213 |
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ddc 510 bkl 31.12 bkl 31.20 misc Skew divided difference operator misc Fomin–Kirillov algebra misc Braided Hopf algebra misc Bruhat order |
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ddc 510 bkl 31.12 bkl 31.20 misc Skew divided difference operator misc Fomin–Kirillov algebra misc Braided Hopf algebra misc Bruhat order |
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ddc 510 bkl 31.12 bkl 31.20 misc Skew divided difference operator misc Fomin–Kirillov algebra misc Braided Hopf algebra misc Bruhat order |
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Elektronische Aufsätze Aufsätze Elektronische Ressource |
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Positive expressions for skew divided difference operators |
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Positive expressions for skew divided difference operators |
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Journal of algebraic combinatorics |
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Liu, Ricky Ini |
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10.1007/s10801-015-0606-1 |
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510 |
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positive expressions for skew divided difference operators |
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Positive expressions for skew divided difference operators |
| abstract |
Abstract For permutations %$v,w \in \mathfrak S_n%$, Macdonald defines the skew divided difference operators %$\partial _{w/v}%$ as the unique linear operators satisfying %$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ%$ for all polynomials %$P%$ and %$Q%$. We prove that %$\partial _{w/v}%$ has a positive expression in terms of divided difference operators %$\partial _{ij}%$ for %$i<j%$. In fact, we prove that the analogous result holds in the Fomin–Kirillov algebra %${\mathcal {E}}_n%$, which settles a conjecture of Kirillov. |
| abstractGer |
Abstract For permutations %$v,w \in \mathfrak S_n%$, Macdonald defines the skew divided difference operators %$\partial _{w/v}%$ as the unique linear operators satisfying %$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ%$ for all polynomials %$P%$ and %$Q%$. We prove that %$\partial _{w/v}%$ has a positive expression in terms of divided difference operators %$\partial _{ij}%$ for %$i<j%$. In fact, we prove that the analogous result holds in the Fomin–Kirillov algebra %${\mathcal {E}}_n%$, which settles a conjecture of Kirillov. |
| abstract_unstemmed |
Abstract For permutations %$v,w \in \mathfrak S_n%$, Macdonald defines the skew divided difference operators %$\partial _{w/v}%$ as the unique linear operators satisfying %$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ%$ for all polynomials %$P%$ and %$Q%$. We prove that %$\partial _{w/v}%$ has a positive expression in terms of divided difference operators %$\partial _{ij}%$ for %$i<j%$. In fact, we prove that the analogous result holds in the Fomin–Kirillov algebra %${\mathcal {E}}_n%$, which settles a conjecture of Kirillov. |
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Positive expressions for skew divided difference operators |
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https://dx.doi.org/10.1007/s10801-015-0606-1 |
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| doi_str |
10.1007/s10801-015-0606-1 |
| up_date |
2024-07-03T18:56:11.158Z |
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