
SIGMA 1 (2005), 016, 7 pages math.QA/0511632
http://dx.doi.org/10.3842/SIGMA.2005.016
Representations of the Quantum Algebra su_{q}(1,1) and Discrete qUltraspherical 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
qultraspherical 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
qultraspherical polynomials.
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