Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


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

Representations of the Quantum Algebra suq(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 suq(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 suq(1,1); representations; discrete q-ultraspherical polynomials.

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