Multivariate Askey–Wilson functions and overlap coefficients
Wolter Groenevelt · Arabian Journal of Mathematics · 2025
Abstract We study certain overlap coefficients appearing in representation theory of the quantum algebra $$\mathcal {U}_q(\mathfrak {sl}_2(\mathbb {C}))$$ U q ( 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 [1]. We use the underlying coalgebra structure to derive q -difference equations satisfied by the multivariate Askey–Wilson functions.