SIGMA 1 (2005), 016, 7 pages      math.QA/0511632      https://doi.org/10.3842/SIGMA.2005.016

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

Valentyna Groza
National Aviation University, 1 Komarov Ave., Kyiv, 03058 Ukraine

Received September 16, 2005, in final form November 09, 2005; Published online November 15, 2005

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.

Key words: Quantum algebra su_q(1,1); representations; discrete q-ultraspherical polynomials.

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