Representations of the quantum algebra su_q(1,1) and discrete q-ultraspherical polynomials

Abstract:
We derive orthogonality relations for discrete q-ultraspherical polynomials and for their duals by means of operators of discrete series representations of the quantum algebra su_q(1,1). Spectra and eigenfunctions of these operators are found explicitly. These eigenfunctions, when normalized, form an orthonormal basis in the representation space.