Convolutions for orthogonal polynomials from Lie and quantum algebra representations

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dc.creatorKoelink, H. T.
dc.creatorVan der Jeugt, J.
dc.date1996-07-09
dc.date.accessioned2026-07-07T09:17:11Z
dc.date.available2026-07-07T09:17:11Z
dc.descriptionThe interpretation of the Meixner-Pollaczek, Meixner and Laguerre polynomials as overlap coefficients in the positive discrete series representations of the Lie algebra su(1,1) and the Clebsch-Gordan decomposition leads to generalisations of the convolution identities for these polynomials. Using the Racah coefficients convolution identities for continuous Hahn, Hahn and Jacobi polynomials are obtained. From the quantised universal enveloping algebra for su(1,1) convolution identities for the Al-Salam and Chihara polynomials and the Askey-Wilson polynomials are derived by using the Clebsch-Gordan and Racah coefficients. For the quantised universal enveloping algebra for su(2) q-Racah polynomials are interpreted as Clebsch-Gordan coefficients, and the linearisation coefficients for a two-parameter family of Askey-Wilson polynomials are derived.
dc.descriptionAMS-TeX, 31 pages
dc.identifierhttps://arxiv.org/abs/q-alg/9607010
dc.identifierhttp://arxiv.org/abs/q-alg/9607010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153578
dc.subjectQuantum Algebra
dc.subject33C80, 33D80
dc.titleConvolutions for orthogonal polynomials from Lie and quantum algebra representations
dc.typetext

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