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 R^2. 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 standar...

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Bibliographic Details
Main Author: Charles F. Dunkl
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2013-06-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
Online Access:http://dx.doi.org/10.3842/SIGMA.2013.043
Description
Summary: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 R^2. 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(B_2) (symmetry group of the square) associated to the (2-dimensional) reflection representation. The algebra has two parameters: k_0, k_1. 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.
ISSN:1815-0659