
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 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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References
 Gasper G., Rahman M., Basic hypergeometric functions,
Cambridge, Cambridge University Press, 1990.
 Klimyk A., Schmüdgen K., Quantum groups and their
representations, Berlin, Springer, 1997.
 Burban I.M., Klimyk A.U., Representations of the quantum algebra
U_{q}(su_{1,1}), J. Phys. A: Math. Gen., 1993, V.26,
21392151.
 Atakishiyev N.M., Klimyk A.U., On discrete
qultraspherical polynomials and their duals, J. Math.
Anal. Appl., 2005, V.306, N 2, 637645, math.CA/0403159.
 Atakishiyev N.M., Klimyk A.U., On
qorthogonal polynomials, dual to little and big qJacobi
polynomials, J. Math. Anal. Appl., 2004, V.294, N 2,
246257, math.CA/0307250.
 Berezanskii Ju.M., Expansions in
eigenfunctions of selfadjoint operators, Providence, RI, American
Mathematical Society, 1968.
 Atakishiyev N.M., Klimyk A.U., Duality of
qpolynomials, orthogonal on countable sets of points,
math.CA/0411249.

