Isomorphisms of type A affine Hecke algebras and multivariable orthogonal polynomials

We examine two isomorphisms between affine Hecke alge-bras of type A associated with parameters q−1, t−1 and q, t. One of them maps the non-symmetric Macdonald polynomi-als 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. 1. Introduction. In several recent works [28]-[29], [9]-[10], eigenstates of the rational (type A) Calogero-Sutherland model have been investigated from an algebraic point of view. In particular it has been shown that the algebra governing the eigenfunctions of the periodic Calogero-Sutherland model (namely the typ