{
  "id": "1610.07097",
  "version": "v1",
  "published": "2016-10-22T21:18:01.000Z",
  "updated": "2016-10-22T21:18:01.000Z",
  "title": "Analysis of the minimal representations of SL(n,R)",
  "authors": [
    "Dehbia Achab"
  ],
  "comment": "28 pages. arXiv admin note: text overlap with arXiv:1103.1614",
  "categories": [
    "math.RT"
  ],
  "abstract": "The minimal representations of SL(n,R) can be realized on a Hilbert space of holomorphic functions. This is the analogue of the Brylinski-Kostant model. They can also be realized on a Hilbert space of homogeneous functions on ${\\bboard R}^n$. This is the analogue of the Kobayashi-Orsted model. We will describe the two realizations and a transformation which maps one model to the other. It can be seen as an analogue of the classical Bargmann transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-22T21:18:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "17C36"
    ],
    "keywords": [
      "minimal representations",
      "hilbert space",
      "brylinski-kostant model",
      "classical bargmann transform",
      "holomorphic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}