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arXiv · 1809.04327

A quantum algebra approach to multivariate Askey-Wilson polynomials

Wolter Groenevelt
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Abstract

We study matrix elements of a change of base 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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BibTeXRIS

Wolter Groenevelt. 2018-09-12. A quantum algebra approach to multivariate Askey-Wilson polynomials. https://doi.org/10.1093/imrn%2Frnz182

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