Multivariable Al-Salam & Carlitz polynomials associated with the type A q-Dunkl kernel

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dc.creatorBaker, T. H.
dc.creatorForrester, P. J.
dc.date1997-06-05
dc.date1997-06-12
dc.date.accessioned2026-07-07T09:08:48Z
dc.date.available2026-07-07T09:08:48Z
dc.descriptionThe 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.
dc.descriptionLaTeX 2.09, 25 pages; the relationship with big q-Jacobi polynomials clarified
dc.identifierhttps://arxiv.org/abs/q-alg/9706006
dc.identifierhttp://arxiv.org/abs/q-alg/9706006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150850
dc.subjectQuantum Algebra
dc.titleMultivariable Al-Salam & Carlitz polynomials associated with the type A q-Dunkl kernel
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