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Symmetry, Integrability and Geometry: Methods and Applications, 2005, Volume 1, 016, 7 pp.
DOI: https://doi.org/10.3842/SIGMA.2005.016 (Mi sigma16) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Representations of the Quantum Algebra $\mathrm{su}_q(1,1)$ and Discrete $q$-Ultraspherical Polynomials

Valentyna Groza

National Aviation University, 1 Komarov Ave., Kyiv, 03058 Ukraine
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DOI: https://doi.org/10.3842/SIGMA.2005.016
Abstract: We derive orthogonality relations for discrete $q$-ultraspherical polynomials and their duals by means of operators of representations of the quantum algebra $\mathrm{su}_q(1,1)$. Spectra and eigenfunctions of these operators are found explicitly. These eigenfunctions, when normalized, form an orthonormal basis in the representation space.
Keywords: Quantum algebra $su_q(1,1)$; representations; discrete $q$-ultraspherical polynomials.
Received: September 16, 2005; in final form November 9, 2005; Published online November 15, 2005
Bibliographic databases:
Document Type: Article
MSC: 17B37; 33D45
Language: English
Citation: Valentyna Groza, “Representations of the Quantum Algebra $\mathrm{su}_q(1,1)$ and Discrete $q$-Ultraspherical Polynomials”, SIGMA, 1 (2005), 016, 7 pp.
Citation in format AMSBIB
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\by Valentyna Groza
\paper Representations of the Quantum Algebra $\mathrm{su}_q(1,1)$ and Discrete $q$-Ultraspherical Polynomials
\jour SIGMA
\yr 2005
\vol 1
\papernumber 016
\totalpages 7
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    		Symmetry, Integrability and Geometry: Methods and Applications
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