Groza, Valentyna Representations of the quantum algebra \(\text{su}_q(1,1)\) and discrete \(q\)-ultraspherical polynomials. (English) Zbl 1128.17013 SIGMA, Symmetry Integrability Geom. Methods Appl. 1, Paper 016, 7 p. (2005). Summary: We derive orthogonality relations for discrete \(q\)-ultraspherical polynomials and their duals by means of operators of representations of the quantum algebra \(\text{su}_q(1,1)\). Spectra and eigenfunctions of these operators are found explicitly. These eigenfunctions, when normalized, form an orthonormal basis in the representation space. MSC: 17B37 Quantum groups (quantized enveloping algebras) and related deformations 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) Keywords:Quantum algebra \(\text{su}_q(1,1)\); representations; discrete \(q\)-ultraspherical polynomials PDFBibTeX XMLCite \textit{V. Groza}, SIGMA, Symmetry Integrability Geom. Methods Appl. 1, Paper 016, 7 p. (2005; Zbl 1128.17013) Full Text: DOI arXiv EuDML EMIS