Isomorphisms of Type a Affine Hecke Algebras and Multivariable Orthogonal Polynomials

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.