A Quantum Algebra Approach to Multivariate Askey-Wilson Polynomials

Journal Article (2021)
Author(s)

Wolter Groenevelt (TU Delft - Analysis)

Research Group
Analysis
DOI related publication
https://doi.org/10.1093/imrn/rnz182
More Info
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Publication Year
2021
Language
English
Research Group
Analysis
Issue number
5
Volume number
2021
Pages (from-to)
3224-3266

Abstract

We study matrix elements of a change of basis between two different bases of representations of the quantum algebra U q(su(1, 1)). The two bases, which are multivariate versions of Al-Salam Chihara polynomials, are eigenfunctions of iterated coproducts of twisted primitive elements. The matrix elements are identified with Gasper and Rahman s multivariate Askey Wilson polynomials, and from this interpretation we derive their orthogonality relations. Furthermore, the matrix elements are shown to be eigenfunctions of the twisted primitive elements after a change of representation, which gives a quantum algebraic derivation of the fact that the multivariate Askey Wilson polynomials are solutions of a multivariate bispectral q-difference problem.

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