Coupling coefficients of $s{u}_q(1,1)$ and multivariate $q$-Racah polynomials

Abstract

Gasper & Rahman's multivariate $q$-Racah polynomials are shown to arise as connection coefficients between families of multivariate $q$-Hahn or $q$-Jacobi polynomials. The families of $q$-Hahn polynomials are constructed as nested Clebsch--Gordan coefficients for the positive-discrete series representations of the quantum algebra $s{u}_q(1,1)$. This gives an interpretation of the multivariate $q$-Racah polynomials in terms of $3nj$ symbols. It is shown that the families of $q$-Hahn polynomials also arise in wavefunctions of $q$-deformed quantum Calogero--Gaudin superintegrable systems.

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References in corpus (5)

• Orthogonal polynomials of several variables
• A higher rank Racah algebra and the ${\mathbb{Z}}_2^n$ Laplace-Dunkl operator
• Embeddings of the Racah Algebra into the Bannai-Ito Algebra
• The generic quantum superintegrable system on the sphere and Racah operators
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Cited by in corpus (5)

• The higher rank $q$-deformed Bannai-Ito and Askey-Wilson algebra
• A higher rank extension of the Askey-Wilson Algebra
• The $q$-Bannai-Ito algebra and multivariate $(-q)$-Racah and Bannai-Ito polynomials
• A quantum algebra approach to multivariate Askey-Wilson polynomials
• An Askey-Wilson Algebra of Rank 2