{
  "id": "1406.3772",
  "version": "v2",
  "published": "2014-06-14T20:58:55.000Z",
  "updated": "2015-01-31T00:39:53.000Z",
  "title": "A new integral formula for Heckman-Opdam hypergeometric functions",
  "authors": [
    "Yi Sun"
  ],
  "comment": "27 pages. v2: added Section 3 on the quasi-classical limit; corrected normalization of Heckman-Opdam hypergeometric functions; added some references",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We provide Harish-Chandra type formulas for the multivariate Bessel functions and Heckman-Opdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the realization of Macdonald polynomials as traces of intertwiners of quantum groups given by Etingof-Kirillov Jr. Integration over the Liouville tori of the Gelfand-Tsetlin integrable system and adjunction for higher Calogero-Moser Hamiltonians recovers and gives a new proof of the integral realization over Gelfand-Tsetlin polytopes which appeared in the recent work of Borodin-Gorin on the beta-Jacobi corners ensemble.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-14T20:58:55.000Z",
      "abstract": "We provide formulas for the multivariate Bessel functions and Heckman-Opdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the realization of Macdonald polynomials as traces of intertwiners of quantum groups given by Etingof and Kirillov Jr. in [EK94]. Integration over the Liouville tori of the Gelfand-Tsetlin integrable system and adjunction for higher Calogero-Moser Hamiltonians relates our expression to the integral realization over Gelfand-Tsetlin polytopes which appeared in the recent work [BG13] of Borodin and Gorin on the beta-Jacobi corners ensemble.",
      "comment": "15 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-31T00:39:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C67",
      "81R12",
      "22E46"
    ],
    "keywords": [
      "heckman-opdam hypergeometric functions",
      "integral formula",
      "higher calogero-moser hamiltonians relates",
      "multivariate bessel functions",
      "macdonald polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.3772S"
    }
  }
}