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Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Vector-Valued Polynomials and a Matrix Weight Function with B₂-Action. II
Інший ID:
2010 Mathematics Subject Classification: 33C52; 33C20
DOI: http://dx.doi.org/10.3842/SIGMA.2013.043
DOI: http://dx.doi.org/10.3842/SIGMA.2013.043
Посилання:
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.
Дата:
2013
Переглядів:
485
Завантажень:
244
Анотація:
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.
