
SIGMA 9 (2013), 043, 11 pages arXiv:1302.3632
http://dx.doi.org/10.3842/SIGMA.2013.043
VectorValued Polynomials and a Matrix Weight Function with B_{2}Action. II
Charles F. Dunkl
Department of Mathematics, University of Virginia, PO Box 400137, Charlottesville VA 229044137, USA
Received February 15, 2013, in final form June 07, 2013; Published online June 12, 2013
Abstract
This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is
a construction of a 2×2 positivedefinite 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 (2dimensional) 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.
Key words:
matrix Gaussian weight function.
pdf (325 kb)
tex (13 kb)
References
 Dunkl C.F., Vectorvalued polynomials and a matrix weight function
with B_{2}action, SIGMA 9 (2013), 007, 23 pages, arXiv:1210.1177.

