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 $E_{ \eta}(x;q^{ -1},t^{ -1})$ onto $E_{ \eta}(x;q,t)$, while the other maps them onto non-symmetric analogues of the multivariable Al-Salam & Carlitz polynomials. Using the properties of $E_{ \eta}(x;q^{ -1},t^{ -1})$, the corresponding properties of these latter polynomials can then be elucidated.
Categories: q-alg math.QA