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

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(...

Full description

Saved in:
Bibliographic Details
Published inSymmetry, integrability and geometry, methods and applications Vol. 4; p. 052
Main Author Koornwinder, Tom H.
Format Journal Article
LanguageEnglish
Published Kiev National Academy of Sciences of Ukraine 01.01.2008
National Academy of Science of Ukraine
Subjects
Askey-Wilson polynomials
double affine Hecke algebra in rank one
spherical subalgebra
Zhedanov's algebra AW
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1815-0659
1815-0659
DOI:10.3842/SIGMA.2008.052