{
  "id": "2309.09693",
  "version": "v1",
  "published": "2023-09-18T11:58:21.000Z",
  "updated": "2023-09-18T11:58:21.000Z",
  "title": "Minimal representations of the metaplectic Lie supergroup and the super Segal-Bargmann transform",
  "authors": [
    "Sam Claerebout"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct a Schr\\\"odinger model and a Fock model of a minimal representation of the metaplectic Lie supergroup $\\mathrm{Mp}(2m|2n,2n)$. Then, we show that the Schr\\\"odinger model of the minimal representation leads to an already known Schr\\\"odinger model of the metaplectic representation of $\\mathrm{Mp}(2m|2n,2n)$. Therefore, the Fock model of the minimal representation allows us to construct a Fock model of this metaplectic representation. We then construct an intertwining super Segal-Bargmann transform which extends the classical Segal-Bargmann transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-18T11:58:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B60",
      "43A32",
      "58C50"
    ],
    "keywords": [
      "metaplectic lie supergroup",
      "minimal representation",
      "fock model",
      "metaplectic representation",
      "intertwining super segal-bargmann transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}