Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra

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dc.creatorKoornwinder, Tom H.
dc.date2007-11-14
dc.date2008-06-10
dc.date.accessioned2026-07-07T09:43:11Z
dc.date.available2026-07-07T09:43:11Z
dc.descriptionThis paper builds on the previous paper arXiv:math/0612730 by the author, where a relationship between Zhedanov's algebra AW(3) and the double affine Hecke algebra (DAHA) corresponding to the Askey-Wilson polynomials was established. It is shown here that the spherical subalgebra of this DAHA is isomorphic to AW(3) with an additional relation that the Casimir operator equals an explicit constant. A similar result with q-shifted parameters holds for the antispherical subalgebra. Some theorems on centralizers and centers for the algebras under consideration will finally be proved as corollaries of the characterization of the spherical and antispherical subalgebra.
dc.descriptionThis is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ In v2 remarks about duality anti-algebra isomorphism and about shift operators added
dc.identifierhttps://arxiv.org/abs/0711.2320
dc.identifierhttp://arxiv.org/abs/0711.2320
dc.identifierSIGMA 4 (2008), 052, 17 pages
dc.identifierdoi:10.3842/SIGMA.2008.052
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162458
dc.subjectQuantum Algebra
dc.subject33D80
dc.titleZhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra
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