{
  "id": "2002.12836",
  "version": "v1",
  "published": "2020-02-28T16:07:52.000Z",
  "updated": "2020-02-28T16:07:52.000Z",
  "title": "A Fock model and the Segal-Bargmann transform for the minimal representation of the orthosymplectic Lie superalgebra $\\mathfrak{osp}(m,2|2n)$",
  "authors": [
    "Sigiswald Barbier",
    "Sam Claerebout",
    "Hendrik De Bie"
  ],
  "comment": "35 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "The minimal representation of a semisimple Lie group is a `small' infinite-dimensional irreducible unitary representation. It is thought to correspond to the minimal nilpotent coadjoint orbit in Kirillov's orbit philosophy. The Segal-Bargmann transform is an intertwining integral transformation between two different models of the minimal representation for Hermitian Lie groups of tube type. In this paper we construct a Fock model for the minimal representation of the orthosymplectic Lie superalgebra $\\mathfrak{osp}(m,2|2n)$. We also construct an integral transform which intertwines the Schr\\\"odinger model for the minimal representation of the orthosymplectic Lie superalgebra $\\mathfrak{osp}(m,2|2n)$ with this new Fock model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-28T16:07:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B60",
      "22E46",
      "58C50"
    ],
    "keywords": [
      "orthosymplectic lie superalgebra",
      "minimal representation",
      "fock model",
      "segal-bargmann transform",
      "minimal nilpotent coadjoint orbit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}