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Vector-Valued Polynomials and a Matrix Weight Function with $B_{2}$-Action. II
Symmetry, integrability and geometry: methods and applications, Tome 9 (2013) Cet article a éte moissonné depuis la source Math-Net.Ru

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This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a $2\times2$ positive-definite matrix function $K (x)$ on $\mathbb{R}^{2}$. 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.
Keywords: matrix Gaussian weight function. 
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     author = {Charles F. Dunkl},
     title = {Vector-Valued {Polynomials} and {a~Matrix} {Weight} {Function} with $B_{2}${-Action.~II}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     volume = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a42/}
}
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Charles F. Dunkl. Vector-Valued Polynomials and a Matrix Weight Function with $B_{2}$-Action. II. Symmetry, integrability and geometry: methods and applications, Tome 9 (2013). http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a42/

[1] Dunkl C. F., “Vector-valued polynomials and a matrix weight function with $B_{2}$-action”, SIGMA, 9 (2013), 007, 23 pp., arXiv: 1210.1177 | DOI | MR