Geodesic
Representations of the Quantum Algebra $\mathrm{su}_q(1,1)$ and Discrete $q$-Ultraspherical Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 1 (2005) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Valentyna Groza},
     title = {Representations of the {Quantum} {Algebra} $\mathrm{su}_q(1,1)$ and {Discrete} $q${-Ultraspherical} {Polynomials}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a15/}
}
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Valentyna Groza. Representations of the Quantum Algebra $\mathrm{su}_q(1,1)$ and Discrete $q$-Ultraspherical Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 1 (2005). http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a15/

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