{
  "id": "2309.12703",
  "version": "v1",
  "published": "2023-09-22T08:28:30.000Z",
  "updated": "2023-09-22T08:28:30.000Z",
  "title": "Irreducible unitary representations with non-zero relative Lie algebra cohomology of the Lie group $SO_0(2,m)$",
  "authors": [
    "Ankita Pal",
    "Pampa Paul"
  ],
  "comment": "20 pages, 2 figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "By a theorem of D. Wigner, an irreducible unitary representation with non-zero $(\\frak{g},K)$-cohomology has trivial infinitesimal character, and hence up to unitary equivalence, these are finite in number. We have determined the number of equivalence classes of these representations and the Poincar\\'{e} polynomial of cohomologies of these representations for the Lie group $SO_0(2,m)$ for any positive integer $m.$ We have also determined, among these, which are discrete series representations and holomorphic discrete series representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-22T08:28:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "17B10",
      "17B20",
      "17B22",
      "17B56"
    ],
    "keywords": [
      "non-zero relative lie algebra cohomology",
      "irreducible unitary representation",
      "lie group",
      "holomorphic discrete series representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}