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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2005
• Main Author: Groza, V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2005
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209344
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Representations of the Quantum Algebra suq(1,1) and Discrete q-Ultraspherical Polynomials / V. Groza // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 7 назв. — англ.

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 i...