2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150850The Al-Salam & Carlitz polynomials are $q$-generalizations of the classical Hermite polynomials. Multivariable generalizations of these polynomials are introduced via a generating function involving a multivariable hypergeometric function which is the $q$-analogue of the type-$A$ Dunkl integral kernel. An eigenoperator is established for these polynomials and this is used to prove orthogonality with respect to a certain Jackson integral inner product. This inner product is normalized by deriving a $q$-analogue of the Mehta integral, and the corresponding normalization of the multivariable Al-Salam & Carlitz polynomials is derived from a Pieri-type formula. Various other special properties of the polynomials are also presented, including their relationship to the shifted Macdonald polynomials and the big $q$-Jacobi polynomials.LaTeX 2.09, 25 pages; the relationship with big q-Jacobi polynomials clarifiedQuantum Algebratext