SIGMA 1 (2005), 016, 7 pages math.QA/0511632
Representations of the Quantum Algebra suq(1,1) and Discrete q-Ultraspherical Polynomials
National Aviation University, 1 Komarov Ave.,
Kyiv, 03058 Ukraine
Received September 16, 2005, in final form November 09, 2005;
Published online November 15, 2005
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.
Quantum algebra suq(1,1); representations; discrete
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