2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/88068We 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.LaTeX2e, 20 pages, minor changes to referencesQuantum Algebratext