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

By Tom H. Koornwinder. 2007

60 citations recorded by the source corpus.

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) corre- sponding 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.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/10c5ca5995fd8c67a7c76bf85e44ea387c482ed5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Paul M. Terwilliger
2. Tatsuro Ito

In Applied Mathematics

1. Paul M. Terwilliger
2. Plamen Iliev
3. Alexei S. Zhedanov
4. Luc Vinet
5. 伊藤 達郎

In Geometry and Topology

1. Paul M. Terwilliger
2. Tatsuro Ito
3. Alexei S. Zhedanov
4. Luc Vinet
5. Plamen Iliev
6. 伊藤 達郎

Citations in the corpus

• The Universal Askey-Wilson Algebra (2011, background): “There is a connection to the double affine Hecke algebra of type (C 1 , C1) [32, 38, 39].”