Bilinear summation formulas from quantum algebra representations

Simple item page
dc.creatorGroenevelt, Wolter
dc.date2002-01-29
dc.date.accessioned2026-07-07T07:35:58Z
dc.date.available2026-07-07T07:35:58Z
dc.descriptionThe tensor product of a positive and a negative discrete series representation of the quantum algebra U_q(su(1,1)) decomposes as a direct integral over the principal unitary series representations. Discrete terms can appear, and these terms are a finite number of discrete series representations, or one complementary series representation. From the interpretation as overlap coefficients of little q-Jacobi functions and Al-Salam and Chihara polynomials in base q and base q^{-1}, two closely related bilinear summation formulas for the Al-Salam and Chihara polynomials are derived. The formulas involve Askey-Wilson polynomials, continuous dual q-Hahn polynomials and little q-Jacobi functions. The realization of the discrete series as q-difference operators on the spaces of holomorphic and anti-holomorphic functions, leads to a bilinear generating function for a certain type of 2-phi-1 -series, which can be considered as a special case of the dual transmutation kernel for little q-Jacobi functions.
dc.description27 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0201272
dc.identifierhttp://arxiv.org/abs/math/0201272
dc.identifierRamanujan J. 8 (2004), no. 3, 383-416
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120276
dc.subjectQuantum Algebra
dc.subjectClassical Analysis and ODEs
dc.subject33D45, 33D80, 20G42
dc.titleBilinear summation formulas from quantum algebra representations
dc.typetext

Files

Collections

arXiv