Askey-Wilson functions and quantum groups

dc.creatorStokman, Jasper V.
dc.date2003-01-28
dc.date.accessioned2026-07-07T04:54:44Z
dc.date.available2026-07-07T04:54:44Z
dc.descriptionEigenfunctions of the Askey-Wilson second order $q$-difference operator for $0<q<1$ and $|q|=1$ are constructed as formal matrix coefficients of the principal series representation of the quantized universal enveloping algebra $U_q(sl(2,\mathbb{C}))$. The eigenfunctions are in integral form and may be viewed as analogues of Euler's integral representation for Gauss' hypergeometric series. We show that for $0<q<1$ the resulting eigenfunction can be rewritten as a very-well-poised ${}_8ϕ_7$-series, and reduces for special parameter values to a natural elliptic analogue of the cosine kernel.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/math/0301330
dc.identifierhttp://arxiv.org/abs/math/0301330
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66374
dc.subjectQuantum Algebra
dc.subjectClassical Analysis and ODEs
dc.subjectRepresentation Theory
dc.titleAskey-Wilson functions and quantum groups
dc.typetext

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