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 are motivated by relations between coproducts twisted primitive elements two-fold tensor product quantum $\mathcal{U}_{q}(\mathfrak{sl}(2,\mathbb C))$. It shown that bivariate $q$-Racah polynomials appear overlap coefficients eigenvectors generators Furthermore, corresponding $q$-difference operators calculated using defining algebra, showing it encodes bispectral properties polynomials.