Isomorphisms of type A affine Hecke algebras and multivariable orthogonal polynomials

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 Eη(x;q-1,t-1) onto Eη(x;q,t), while the other maps them onto non-symmetric analogues of the multivariable Al-Salam & Carlitz polynomials. Using the properties of Eη(x;q-1,t-1), the corresponding properties of these latter polynomials can then be elucidated.