An Askey-Wilson Algebra of Rank 2

Abstract

An algebra is introduced which can be considered as a rank 2 extension of the Askey-Wilson algebra. Relations in this algebra are motivated by relations between coproducts of twisted primitive elements in the two-fold tensor product of the quantum algebra 𝒰𝑞(𝔰𝔩(2, ℂ)). It is shown that bivariate 𝑞-Racah polynomials appear as overlap coefficients of eigenvectors of generators of the algebra. Furthermore, the corresponding 𝑞-difference operators are calculated using the defining relations of the algebra, showing that it encodes the bispectral properties of the bivariate 𝑞-Racah polynomials.