Vector-Valued Polynomials and a Matrix Weight Function with B 2 -Action. II

[摘要] 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 3 F 2 -type is derived and used for the proof.

[关键词] matrix Gaussian weight function