SIGMA 9 (2013), 043, 11 pages arXiv:1302.3632
Vector-Valued Polynomials and a Matrix Weight Function with B2-Action. II
Charles F. Dunkl
Department of Mathematics, University of Virginia, PO Box 400137, Charlottesville VA 22904-4137, USA
Received February 15, 2013, in final form June 07, 2013; Published online June 12, 2013
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.
matrix Gaussian weight function.
pdf (325 kb)
tex (13 kb)
- Dunkl C.F., Vector-valued polynomials and a matrix weight function
with B2-action, SIGMA 9 (2013), 007, 23 pages, arXiv:1210.1177.