Representations of the quantum algebra \(\text{su}_q(1,1)\) and discrete \(q\)-ultraspherical polynomials

DOI10.3842/SIGMA.2005.016zbMATH Open1128.17013arXivmath/0511632MaRDI QIDQ2495130

V. A. Groza

Publication date: 4 July 2006

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/math/0511632

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zbMATH Keywords

representationsdiscrete \(q\)-ultraspherical polynomialsQuantum algebra \(\text{su}_q(1,1)\)

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

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