The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case

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dc.creatorKoornwinder, Tom H.
dc.date2006-12-22
dc.date2007-11-07
dc.date.accessioned2026-07-07T09:34:34Z
dc.date.available2026-07-07T09:34:34Z
dc.descriptionZhedanov's algebra AW(3) is considered with explicit structure constants such that, in the basic representation, the first generator becomes the second order q-difference operator for the Askey-Wilson polynomials. It is proved that this representation is faithful for a certain quotient of AW(3) such that the Casimir operator is equal to a special constant. Some explicit aspects of the double affine Hecke algebra (DAHA) related to symmetric and non-symmetric Askey-Wilson polynomials are presented and proved without requiring knowledge of general DAHA theory. Finally a central extension of this quotient of AW(3) is introduced which can be embedded in the DAHA by means of the faithful basic representations of both algebras.
dc.descriptionThis is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ In v4 a slight error in formula (2.8) for Q_0 is corrected
dc.identifierhttps://arxiv.org/abs/math/0612730
dc.identifierhttp://arxiv.org/abs/math/0612730
dc.identifierSIGMA 3 (2007), 063, 15 pages
dc.identifierdoi:10.3842/SIGMA.2007.063
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159537
dc.subjectQuantum Algebra
dc.subjectClassical Analysis and ODEs
dc.subject33D80; 33D45
dc.titleThe Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case
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