Coupling coefficients of su 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 suq(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.