Wilson function transforms related to Racah coefficients
type: Item
instance of: scholarly article
title: Wilson function transforms related to Racah coefficients
zbMATH Open document ID: 1102.33009
published in: Acta Applicandae Mathematicae
publication date: 2006-09-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0501511
review text: The irreducible \(*\)-representations of the Lie algebra su\((1,1)\) consist of discrete series representations, principal unitary series and complementary series. The author computes Racah coefficients for tensor products of representations where at least two of them belong to the discrete series. This is done by using explicit expressions for the Clebsch-Gordan coefficients in terms of hypergeometric functions. It turns out that the Racah coefficients are Wilson polynomials and functions which lead to a natural interpretation of the integral transforms with Wilson functions as kernels. As further applications, several identities on sums and integrals of Wilson functions are given. Moreover, it is shown that the same procedure for the quantizized universal enveloping algebra \(U_q(\text{su}(1,1))\) leads to Askey-Wilson functions and polynomials.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 33D45
Mathematics Subject Classification ID: 33D80
zbMATH DE Number: 5051226
zbMATH Keywords: Askey-Wilson polynomials
zbMATH Keywords: integral transforms
zbMATH Keywords: Racah coefficients
zbMATH Keywords: representation theory
zbMATH Keywords: Wilson functions
author: Wolter Groenevelt
reviewed by: Michael Voit
MaRDI profile type: Publication
OpenAlex ID: W2141445432
arXiv ID: math/0501511
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DOI: 10.1007/S10440-006-9024-7
description: scientific article