Representations of the Quantum Algebra suq(1,1) and Discrete q-Ultraspherical Polynomials

Abstract

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