A note on tensor products of \(q\)-algebra representations and orthogonal polynomials
type: Item
instance of: scholarly article
title: A note on tensor products of \(q\)-algebra representations and orthogonal polynomials
zbMATH Open document ID: 0864.33016
DOI: 10.1016/0377-0427(95)00252-9
published in: Journal of Computational and Applied Mathematics
publication date: 1997-06-10T00:00:00Z
review text: The authors have given examples of tensor products of distinct generalized \(Sl_q(2)\) algebras with a factor from the positive discrete series of representations of one algebra and a factor from the negative discrete series of the other. The authors have also shown the equation for the common eigenfunctions of the Casimir operator and the Cartan subalgebra generator is a three term recurrence relation corresponding to orthogonality for special cases of the Askey-Wilson polynomials and this connection yields a resolution of the tensor product representation into a direct integral of irreducible representation. Further, an identity for the matrix elements of the ``group representation operators'' with respect to the tensor product and the reduced bases follows easily has also been studied.
Mathematics Subject Classification ID: 33D60
Mathematics Subject Classification ID: 33D45
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 908392
zbMATH Keywords: \(q\)-algebras
zbMATH Keywords: quantum groups
zbMATH Keywords: Askey-Wilson polynomials
author: Ernest G. Kalnins
author: W. jun. Miller
reviewed by: P. K. Mital
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00252-9
OpenAlex ID: W2049709918
cites work: Q4040884
cites work: Models of q-algebra representations: Tensor products of special unitary and oscillator algebras
cites work: Models of q-algebra representations: Matrix elements of the q-oscillator algebra
cites work: Models ofQ-Algebra Representations: The Group of Plane Motions
cites work: The Addition Formula for Continuousq-Legendre Polynomials and Associated Spherical Elements on the $SU(2)$ Quantum Group Related to Askey–Wilson Polynomials
cites work: The q-analogue of the Laguerre polynomials
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description: scientific article; zbMATH DE number 908392