{
  "annotation_id": "76e51d28-d3a4-45c0-ac3d-b09105049f53",
  "date_created": "2026-03-02T18:01:27.730000Z",
  "date_modified": "2026-03-02T18:01:27.730000Z",
  "file_hash": "aa17a911b789a1ed1bab91fc686b2fd6cffea809c9cec89e5e582c477c64636d",
  "private": false,
  "record": {
    "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",
  "source": {
    "execution_id": "d0f76c25-2f2e-4583-a231-f48ebdb08499",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}