Vector-Valued Polynomials and a Matrix Weight Function with B2-Action. II

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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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:
matrix Gaussian weight function
Online Access:http://dx.doi.org/10.3842/SIGMA.2013.043
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spelling doaj-73b704baf02544378a52398d4f63213c2020-11-24T23:05:43ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592013-06-01904310.3842/SIGMA.2013.043Vector-Valued Polynomials and a Matrix Weight Function with B2-Action. IICharles F. DunklThis 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. http://dx.doi.org/10.3842/SIGMA.2013.043matrix Gaussian weight function
collection DOAJ
language English
format Article
sources DOAJ
author Charles F. Dunkl
spellingShingle Charles F. Dunkl
Vector-Valued Polynomials and a Matrix Weight Function with B2-Action. II
Symmetry, Integrability and Geometry: Methods and Applications
matrix Gaussian weight function
author_facet Charles F. Dunkl
author_sort Charles F. Dunkl
title Vector-Valued Polynomials and a Matrix Weight Function with B2-Action. II
title_short Vector-Valued Polynomials and a Matrix Weight Function with B2-Action. II
title_full Vector-Valued Polynomials and a Matrix Weight Function with B2-Action. II
title_fullStr Vector-Valued Polynomials and a Matrix Weight Function with B2-Action. II
title_full_unstemmed Vector-Valued Polynomials and a Matrix Weight Function with B2-Action. II
title_sort vector-valued polynomials and a matrix weight function with b2-action. ii
publisher National Academy of Science of Ukraine
series Symmetry, Integrability and Geometry: Methods and Applications
issn 1815-0659
publishDate 2013-06-01
description 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.
topic matrix Gaussian weight function
url http://dx.doi.org/10.3842/SIGMA.2013.043
work_keys_str_mv AT charlesfdunkl vectorvaluedpolynomialsandamatrixweightfunctionwithb2actionii
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