An Askey-Wilson Algebra of Rank 2

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 qdifference operators are calculated using the defining relations of the algebra, showing that it encodes the bispectral properties of the bivariate q-Racah polynomials.