{
  "id": "2305.15892",
  "version": "v1",
  "published": "2023-05-25T09:45:53.000Z",
  "updated": "2023-05-25T09:45:53.000Z",
  "title": "On the classification of unitary highest weight modules",
  "authors": [
    "Pavle Pandžić",
    "Ana Prlić",
    "Vladimír Souček",
    "Vít Tuček"
  ],
  "comment": "31 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "In the 1980s, Enright, Howe and Wallach [EHW] and independently Jakobsen [J] gave a complete classification of the unitary highest weight modules. In this paper we give a more direct and elementary proof of the same result for the (universal covers of the) Lie groups $Sp(2n, \\mathbb{R}), SO^{*}(2n)$ and $SU(p, q)$. We also show how to describe the set of unitary highest weight modules with a given infinitesimal character.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-25T09:45:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E47"
    ],
    "keywords": [
      "unitary highest weight modules",
      "complete classification",
      "elementary proof",
      "universal covers",
      "lie groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}