Isomorphisms of type A affine Hecke algebras and multivariable orthogonal polynomials

T.H. Baker and P.J. Forrester

Vol. 194 (2000), No. 1, 19–41

DOI: 10.2140/pjm.2000.194.19

Abstract

We examine two isomorphisms between affine Hecke algebras of type A associated with parameters q⁻¹, t⁻¹ and q, t. One of them maps the non-symmetric Macdonald polynomials E_η(x;q⁻¹,t⁻¹) onto E_η(x;q,t), while the other maps them onto non-symmetric analogues of the multivariable Al-Salam & Carlitz polynomials. Using the properties of E_η(x;q⁻¹ ,t⁻¹), the corresponding properties of these latter polynomials can then be elucidated.

Milestones

Received: 9 December 1997

Revised: 25 June 1999

Published: 1 May 2000