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Multivariate Askey-Wilson functions and overlap coefficients

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arxiv 2504.09735 v1 pith:2INANRAF submitted 2025-04-13 math.QA math.CA

Wolter Groenevelt This is my paper · ORCID
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keywords askey-wilsonfunctionscoefficientsmultivariateoverlapalgebraalgebraicappearing
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abstract

We study certain overlap coefficients appearing in representation theory of the quantum algebra $\U_q(\mathfrak{sl}_2(\C))$. The overlap coefficients can be identified as products of Askey-Wilson functions, leading to an algebraic interpretation of the multivariate Askey-Wilson functions introduced by Geronimo and Iliev. We use the underlying coalgebra structure to derive $q$-difference equations satisfied by the multivariate Askey-Wilson functions.

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  1. The quantum loop algebra of $sl_2$ and $q$-Racah type bivariate functions

    math.QA 2026-07 conditional novelty 6.0 of 10

    Bivariate q-Racah-type functions are realized as overlaps of six distinguished eigenbases in tensor-product evaluation representations of L U_q sl2, one family linked to tridiagonal pairs and another conjecturally to ...

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