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

Valentyna Groza
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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.

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BibTeXRIS

Valentyna Groza. 2005-11-25. Representations of the Quantum Algebra su_q(1,1) and Discrete q-Ultraspherical Polynomials. https://doi.org/10.3842/sigma.2005.016

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