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 their duals by means of operators of 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.

Keywords

• quantum algebra su_q(1
• 1)
• representations
• discrete q-ultraspherical polynomials