2007/11/30 by Tom H. Koornwinder
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Mathematical functions and polynomials #math.QA #msc:33D80
paper · pdf · doi:10.3842/sigma.2008.052
published as SIGMA 4 (2008), 052, 17 pages · This 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
arxiv created 2008/06/10 · openalex publication_date 2008/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper builds on the previous paper 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.