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

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

2005-11-25

arxiv.org/abs/math/0511632v1

SIGMA 1 (2005), 016, 7 pages

Mathematics

Quantum Algebra

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2005.016

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.

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