Askey-Wilson polynomials: an affine Hecke algebraic approach

Simple item page
dc.creatorNoumi, Masatoshi
dc.creatorStokman, Jasper V.
dc.date2000-01-06
dc.date.accessioned2026-07-07T04:33:14Z
dc.date.available2026-07-07T04:33:14Z
dc.descriptionWe study Askey-Wilson type polynomials using representation theory of the double affine Hecke algebra. In particular, we prove bi-orthogonality relations for non-symmetric and anti-symmetric Askey-Wilson polynomials with respect to a complex measure. We give duality properties of the non-symmetric Askey-Wilson polynomials, and we show how the non-symmetric Askey-Wilson polynomials can be created from Sahi's intertwiners. The diagonal terms associated to the bi-orthogonality relations (which replace the notion of quadratic norm evaluations for orthogonal polynomials) are expressed in terms of residues of the complex weight function using intertwining properties of the non-symmetric Askey-Wilson transform under the action of the double affine Hecke algebra. We evaluate the constant term, which is essentially the well-known Askey-Wilson integral, using shift operators. We furthermore show how these results reduce to well-known properties of the symmetric Askey-Wilson polynomials, as were originally derived by Askey and Wilson using basic hypergeometric series theory.
dc.description35 pages
dc.identifierhttps://arxiv.org/abs/math/0001033
dc.identifierhttp://arxiv.org/abs/math/0001033
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58496
dc.subjectQuantum Algebra
dc.subjectClassical Analysis and ODEs
dc.subjectRepresentation Theory
dc.subject33D45, 33D80
dc.titleAskey-Wilson polynomials: an affine Hecke algebraic approach
dc.typetext

Files

Collections

arXiv