Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II
This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a 2×2 positive-definite matrix function K(x) on R². The entries of K(x) are expressed in terms of hypergeometric functions. This matrix is used in the formula for a Gaussian inner product related to the standard...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
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| Format: | Artikel |
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Інститут математики НАН України
2013
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| Zitieren: | Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 1 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862557672768798720 |
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| author | Dunkl, C.F. |
| author_facet | Dunkl, C.F. |
| citation_txt | Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 1 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a 2×2 positive-definite matrix function K(x) on R². The entries of K(x) are expressed in terms of hypergeometric functions. This matrix is used in the formula for a Gaussian inner product related to the standard module of the rational Cherednik algebra for the group W(B₂) (symmetry group of the square) associated to the (2-dimensional) reflection representation. The algebra has two parameters: k₀, k₁. In the previous paper K is determined up to a scalar, namely, the normalization constant. The conjecture stated there is proven in this note. An asymptotic formula for a sum of ₃F₂-type is derived and used for the proof.
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| first_indexed | 2025-11-25T22:45:07Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149200 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T22:45:07Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
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| spelling | Dunkl, C.F. 2019-02-19T18:33:28Z 2019-02-19T18:33:28Z 2013 Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 1 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C52; 33C20 DOI: http://dx.doi.org/10.3842/SIGMA.2013.043 https://nasplib.isofts.kiev.ua/handle/123456789/149200 This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a 2×2 positive-definite matrix function K(x) on R². The entries of K(x) are expressed in terms of hypergeometric functions. This matrix is used in the formula for a Gaussian inner product related to the standard module of the rational Cherednik algebra for the group W(B₂) (symmetry group of the square) associated to the (2-dimensional) reflection representation. The algebra has two parameters: k₀, k₁. In the previous paper K is determined up to a scalar, namely, the normalization constant. The conjecture stated there is proven in this note. An asymptotic formula for a sum of ₃F₂-type is derived and used for the proof. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II Article published earlier |
| spellingShingle | Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II Dunkl, C.F. |
| title | Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II |
| title_full | Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II |
| title_fullStr | Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II |
| title_full_unstemmed | Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II |
| title_short | Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II |
| title_sort | vector-valued polynomials and a matrix weight function with b₂-action. ii |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149200 |
| work_keys_str_mv | AT dunklcf vectorvaluedpolynomialsandamatrixweightfunctionwithb2actionii |