On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$
Abstract Kostant’s weight q-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the q-analog of Kostant’s partition function. The q-analog of the partition function is a polynomial-valued function defined by %$\wp _q(\xi )=\sum _{i=0}^k c_i q^i...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Harris, Pamela E. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Applicable algebra in engineering, communication and computing - Berlin : Springer, 1990, 35(2022), 2 vom: 31. März, Seite 253-289 |
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| Übergeordnetes Werk: |
volume:35 ; year:2022 ; number:2 ; day:31 ; month:03 ; pages:253-289 |
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| DOI / URN: |
10.1007/s00200-022-00546-7 |
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| Katalog-ID: |
SPR054847001 |
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| 100 | 1 | |a Harris, Pamela E. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ |
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| 520 | |a Abstract Kostant’s weight q-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the q-analog of Kostant’s partition function. The q-analog of the partition function is a polynomial-valued function defined by %$\wp _q(\xi )=\sum _{i=0}^k c_i q^i%$, where %$c_i%$ is the number of ways the weight %$\xi%$ can be written as a sum of exactly i positive roots of a Lie algebra %${\mathfrak {g}}%$. The evaluation of the q-multiplicity formula at %$q = 1%$ recovers the multiplicity of a weight in an irreducible highest weight representation of %${\mathfrak {g}}%$. In this paper, we specialize to the Lie algebra %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ and we provide a closed formula for the q-analog of Kostant’s partition function, which extends recent results of Shahi, Refaghat, and Marefat. We also describe the supporting sets of the multiplicity formula (known as the Weyl alternation sets of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$), and use these results to provide a closed formula for the q-multiplicity for any pair of dominant integral weights of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$. Throughout this work, we provide code to facilitate these computations. | ||
| 650 | 4 | |a -analog of Kostant’s partition function |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -weight multiplicities |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Hollander, Peter |4 aut | |
| 700 | 1 | |a Qin, Daniel C. |4 aut | |
| 700 | 1 | |a Rodriguez-Hertz, Maria |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Applicable algebra in engineering, communication and computing |d Berlin : Springer, 1990 |g 35(2022), 2 vom: 31. März, Seite 253-289 |w (DE-627)253389909 |w (DE-600)1458434-7 |x 1432-0622 |7 nnns |
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10.1007/s00200-022-00546-7 doi (DE-627)SPR054847001 (SPR)s00200-022-00546-7-e DE-627 ger DE-627 rakwb eng Harris, Pamela E. verfasserin aut On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 Abstract Kostant’s weight q-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the q-analog of Kostant’s partition function. The q-analog of the partition function is a polynomial-valued function defined by %$\wp _q(\xi )=\sum _{i=0}^k c_i q^i%$, where %$c_i%$ is the number of ways the weight %$\xi%$ can be written as a sum of exactly i positive roots of a Lie algebra %${\mathfrak {g}}%$. The evaluation of the q-multiplicity formula at %$q = 1%$ recovers the multiplicity of a weight in an irreducible highest weight representation of %${\mathfrak {g}}%$. In this paper, we specialize to the Lie algebra %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ and we provide a closed formula for the q-analog of Kostant’s partition function, which extends recent results of Shahi, Refaghat, and Marefat. We also describe the supporting sets of the multiplicity formula (known as the Weyl alternation sets of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$), and use these results to provide a closed formula for the q-multiplicity for any pair of dominant integral weights of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$. Throughout this work, we provide code to facilitate these computations. -analog of Kostant’s partition function (dpeaa)DE-He213 -weight multiplicities (dpeaa)DE-He213 Hollander, Peter aut Qin, Daniel C. aut Rodriguez-Hertz, Maria aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 35(2022), 2 vom: 31. März, Seite 253-289 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:35 year:2022 number:2 day:31 month:03 pages:253-289 https://dx.doi.org/10.1007/s00200-022-00546-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_101 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_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_4277 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 AR 35 2022 2 31 03 253-289 |
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10.1007/s00200-022-00546-7 doi (DE-627)SPR054847001 (SPR)s00200-022-00546-7-e DE-627 ger DE-627 rakwb eng Harris, Pamela E. verfasserin aut On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 Abstract Kostant’s weight q-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the q-analog of Kostant’s partition function. The q-analog of the partition function is a polynomial-valued function defined by %$\wp _q(\xi )=\sum _{i=0}^k c_i q^i%$, where %$c_i%$ is the number of ways the weight %$\xi%$ can be written as a sum of exactly i positive roots of a Lie algebra %${\mathfrak {g}}%$. The evaluation of the q-multiplicity formula at %$q = 1%$ recovers the multiplicity of a weight in an irreducible highest weight representation of %${\mathfrak {g}}%$. In this paper, we specialize to the Lie algebra %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ and we provide a closed formula for the q-analog of Kostant’s partition function, which extends recent results of Shahi, Refaghat, and Marefat. We also describe the supporting sets of the multiplicity formula (known as the Weyl alternation sets of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$), and use these results to provide a closed formula for the q-multiplicity for any pair of dominant integral weights of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$. Throughout this work, we provide code to facilitate these computations. -analog of Kostant’s partition function (dpeaa)DE-He213 -weight multiplicities (dpeaa)DE-He213 Hollander, Peter aut Qin, Daniel C. aut Rodriguez-Hertz, Maria aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 35(2022), 2 vom: 31. März, Seite 253-289 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:35 year:2022 number:2 day:31 month:03 pages:253-289 https://dx.doi.org/10.1007/s00200-022-00546-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_101 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_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_4277 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 AR 35 2022 2 31 03 253-289 |
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10.1007/s00200-022-00546-7 doi (DE-627)SPR054847001 (SPR)s00200-022-00546-7-e DE-627 ger DE-627 rakwb eng Harris, Pamela E. verfasserin aut On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 Abstract Kostant’s weight q-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the q-analog of Kostant’s partition function. The q-analog of the partition function is a polynomial-valued function defined by %$\wp _q(\xi )=\sum _{i=0}^k c_i q^i%$, where %$c_i%$ is the number of ways the weight %$\xi%$ can be written as a sum of exactly i positive roots of a Lie algebra %${\mathfrak {g}}%$. The evaluation of the q-multiplicity formula at %$q = 1%$ recovers the multiplicity of a weight in an irreducible highest weight representation of %${\mathfrak {g}}%$. In this paper, we specialize to the Lie algebra %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ and we provide a closed formula for the q-analog of Kostant’s partition function, which extends recent results of Shahi, Refaghat, and Marefat. We also describe the supporting sets of the multiplicity formula (known as the Weyl alternation sets of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$), and use these results to provide a closed formula for the q-multiplicity for any pair of dominant integral weights of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$. Throughout this work, we provide code to facilitate these computations. -analog of Kostant’s partition function (dpeaa)DE-He213 -weight multiplicities (dpeaa)DE-He213 Hollander, Peter aut Qin, Daniel C. aut Rodriguez-Hertz, Maria aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 35(2022), 2 vom: 31. März, Seite 253-289 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:35 year:2022 number:2 day:31 month:03 pages:253-289 https://dx.doi.org/10.1007/s00200-022-00546-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_101 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_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_4277 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 AR 35 2022 2 31 03 253-289 |
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10.1007/s00200-022-00546-7 doi (DE-627)SPR054847001 (SPR)s00200-022-00546-7-e DE-627 ger DE-627 rakwb eng Harris, Pamela E. verfasserin aut On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 Abstract Kostant’s weight q-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the q-analog of Kostant’s partition function. The q-analog of the partition function is a polynomial-valued function defined by %$\wp _q(\xi )=\sum _{i=0}^k c_i q^i%$, where %$c_i%$ is the number of ways the weight %$\xi%$ can be written as a sum of exactly i positive roots of a Lie algebra %${\mathfrak {g}}%$. The evaluation of the q-multiplicity formula at %$q = 1%$ recovers the multiplicity of a weight in an irreducible highest weight representation of %${\mathfrak {g}}%$. In this paper, we specialize to the Lie algebra %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ and we provide a closed formula for the q-analog of Kostant’s partition function, which extends recent results of Shahi, Refaghat, and Marefat. We also describe the supporting sets of the multiplicity formula (known as the Weyl alternation sets of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$), and use these results to provide a closed formula for the q-multiplicity for any pair of dominant integral weights of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$. Throughout this work, we provide code to facilitate these computations. -analog of Kostant’s partition function (dpeaa)DE-He213 -weight multiplicities (dpeaa)DE-He213 Hollander, Peter aut Qin, Daniel C. aut Rodriguez-Hertz, Maria aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 35(2022), 2 vom: 31. März, Seite 253-289 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:35 year:2022 number:2 day:31 month:03 pages:253-289 https://dx.doi.org/10.1007/s00200-022-00546-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_101 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_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_4277 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 AR 35 2022 2 31 03 253-289 |
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10.1007/s00200-022-00546-7 doi (DE-627)SPR054847001 (SPR)s00200-022-00546-7-e DE-627 ger DE-627 rakwb eng Harris, Pamela E. verfasserin aut On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 Abstract Kostant’s weight q-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the q-analog of Kostant’s partition function. The q-analog of the partition function is a polynomial-valued function defined by %$\wp _q(\xi )=\sum _{i=0}^k c_i q^i%$, where %$c_i%$ is the number of ways the weight %$\xi%$ can be written as a sum of exactly i positive roots of a Lie algebra %${\mathfrak {g}}%$. The evaluation of the q-multiplicity formula at %$q = 1%$ recovers the multiplicity of a weight in an irreducible highest weight representation of %${\mathfrak {g}}%$. In this paper, we specialize to the Lie algebra %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ and we provide a closed formula for the q-analog of Kostant’s partition function, which extends recent results of Shahi, Refaghat, and Marefat. We also describe the supporting sets of the multiplicity formula (known as the Weyl alternation sets of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$), and use these results to provide a closed formula for the q-multiplicity for any pair of dominant integral weights of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$. Throughout this work, we provide code to facilitate these computations. -analog of Kostant’s partition function (dpeaa)DE-He213 -weight multiplicities (dpeaa)DE-He213 Hollander, Peter aut Qin, Daniel C. aut Rodriguez-Hertz, Maria aut Enthalten in Applicable algebra in engineering, communication and computing Berlin : Springer, 1990 35(2022), 2 vom: 31. März, Seite 253-289 (DE-627)253389909 (DE-600)1458434-7 1432-0622 nnns volume:35 year:2022 number:2 day:31 month:03 pages:253-289 https://dx.doi.org/10.1007/s00200-022-00546-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_101 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_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_4277 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 AR 35 2022 2 31 03 253-289 |
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Enthalten in Applicable algebra in engineering, communication and computing 35(2022), 2 vom: 31. März, Seite 253-289 volume:35 year:2022 number:2 day:31 month:03 pages:253-289 |
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Enthalten in Applicable algebra in engineering, communication and computing 35(2022), 2 vom: 31. März, Seite 253-289 volume:35 year:2022 number:2 day:31 month:03 pages:253-289 |
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The q-analog of the partition function is a polynomial-valued function defined by %$\wp _q(\xi )=\sum _{i=0}^k c_i q^i%$, where %$c_i%$ is the number of ways the weight %$\xi%$ can be written as a sum of exactly i positive roots of a Lie algebra %${\mathfrak {g}}%$. The evaluation of the q-multiplicity formula at %$q = 1%$ recovers the multiplicity of a weight in an irreducible highest weight representation of %${\mathfrak {g}}%$. In this paper, we specialize to the Lie algebra %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ and we provide a closed formula for the q-analog of Kostant’s partition function, which extends recent results of Shahi, Refaghat, and Marefat. We also describe the supporting sets of the multiplicity formula (known as the Weyl alternation sets of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$), and use these results to provide a closed formula for the q-multiplicity for any pair of dominant integral weights of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$. 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Harris, Pamela E. |
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Harris, Pamela E. misc -analog of Kostant’s partition function misc -weight multiplicities On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ |
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On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ -analog of Kostant’s partition function (dpeaa)DE-He213 -weight multiplicities (dpeaa)DE-He213 |
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misc -analog of Kostant’s partition function misc -weight multiplicities |
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On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ |
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On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ |
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on kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {c}})%$ |
| title_auth |
On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ |
| abstract |
Abstract Kostant’s weight q-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the q-analog of Kostant’s partition function. The q-analog of the partition function is a polynomial-valued function defined by %$\wp _q(\xi )=\sum _{i=0}^k c_i q^i%$, where %$c_i%$ is the number of ways the weight %$\xi%$ can be written as a sum of exactly i positive roots of a Lie algebra %${\mathfrak {g}}%$. The evaluation of the q-multiplicity formula at %$q = 1%$ recovers the multiplicity of a weight in an irreducible highest weight representation of %${\mathfrak {g}}%$. In this paper, we specialize to the Lie algebra %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ and we provide a closed formula for the q-analog of Kostant’s partition function, which extends recent results of Shahi, Refaghat, and Marefat. We also describe the supporting sets of the multiplicity formula (known as the Weyl alternation sets of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$), and use these results to provide a closed formula for the q-multiplicity for any pair of dominant integral weights of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$. Throughout this work, we provide code to facilitate these computations. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 |
| abstractGer |
Abstract Kostant’s weight q-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the q-analog of Kostant’s partition function. The q-analog of the partition function is a polynomial-valued function defined by %$\wp _q(\xi )=\sum _{i=0}^k c_i q^i%$, where %$c_i%$ is the number of ways the weight %$\xi%$ can be written as a sum of exactly i positive roots of a Lie algebra %${\mathfrak {g}}%$. The evaluation of the q-multiplicity formula at %$q = 1%$ recovers the multiplicity of a weight in an irreducible highest weight representation of %${\mathfrak {g}}%$. In this paper, we specialize to the Lie algebra %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ and we provide a closed formula for the q-analog of Kostant’s partition function, which extends recent results of Shahi, Refaghat, and Marefat. We also describe the supporting sets of the multiplicity formula (known as the Weyl alternation sets of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$), and use these results to provide a closed formula for the q-multiplicity for any pair of dominant integral weights of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$. Throughout this work, we provide code to facilitate these computations. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 |
| abstract_unstemmed |
Abstract Kostant’s weight q-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the q-analog of Kostant’s partition function. The q-analog of the partition function is a polynomial-valued function defined by %$\wp _q(\xi )=\sum _{i=0}^k c_i q^i%$, where %$c_i%$ is the number of ways the weight %$\xi%$ can be written as a sum of exactly i positive roots of a Lie algebra %${\mathfrak {g}}%$. The evaluation of the q-multiplicity formula at %$q = 1%$ recovers the multiplicity of a weight in an irreducible highest weight representation of %${\mathfrak {g}}%$. In this paper, we specialize to the Lie algebra %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ and we provide a closed formula for the q-analog of Kostant’s partition function, which extends recent results of Shahi, Refaghat, and Marefat. We also describe the supporting sets of the multiplicity formula (known as the Weyl alternation sets of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$), and use these results to provide a closed formula for the q-multiplicity for any pair of dominant integral weights of %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$. Throughout this work, we provide code to facilitate these computations. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 |
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On Kostant’s weight q-multiplicity formula for %${{\mathfrak {s}}}{{\mathfrak {p}}}_6({\mathbb {C}})%$ |
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https://dx.doi.org/10.1007/s00200-022-00546-7 |
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Hollander, Peter Qin, Daniel C. Rodriguez-Hertz, Maria |
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Hollander, Peter Qin, Daniel C. Rodriguez-Hertz, Maria |
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| doi_str |
10.1007/s00200-022-00546-7 |
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2024-07-04T03:14:44.114Z |
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| score |
7.3982344 |