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 |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149200 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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| ISSN: | 1815-0659 |