dorsal/arxiv
View SchemaMultivariable Al-Salam & Carlitz polynomials associated with the type A q-Dunkl kernel
| Authors | T. H. Baker, P. J. Forrester |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9706006 |
| URL | https://arxiv.org/abs/q-alg/9706006 |
Abstract
The 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.
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"abstract": "The Al-Salam \u0026 Carlitz polynomials are $q$-generalizations of the classical\nHermite polynomials. Multivariable generalizations of these polynomials are\nintroduced via a generating function involving a multivariable hypergeometric\nfunction which is the $q$-analogue of the type-$A$ Dunkl integral kernel. An\neigenoperator is established for these polynomials and this is used to prove\northogonality with respect to a certain Jackson integral inner product. This\ninner product is normalized by deriving a $q$-analogue of the Mehta integral,\nand the corresponding normalization of the multivariable Al-Salam \u0026 Carlitz\npolynomials is derived from a Pieri-type formula. Various other special\nproperties of the polynomials are also presented, including their relationship\nto the shifted Macdonald polynomials and the big $q$-Jacobi polynomials.",
"arxiv_id": "q-alg/9706006",
"authors": [
"T. H. Baker",
"P. J. Forrester"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Multivariable Al-Salam \u0026 Carlitz polynomials associated with the type A q-Dunkl kernel",
"url": "https://arxiv.org/abs/q-alg/9706006"
},
"schema_id": "dorsal/arxiv",
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