{
  "id": "2002.10928",
  "version": "v1",
  "published": "2020-02-25T15:02:57.000Z",
  "updated": "2020-02-25T15:02:57.000Z",
  "title": "Representations having vectors fixed by a Levi subgroup",
  "authors": [
    "Ilia Smilga"
  ],
  "comment": "63 pages, 8 tables, 3 figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "For any semisimple real Lie algebra $\\mathfrak{g}_\\mathbb{R}$, we classify the representations of $\\mathfrak{g}_\\mathbb{R}$ that have at least one nonzero vector on which the centralizer of a Cartan subspace, also known as the centralizer of a maximal split torus, acts trivially. In the process, we revisit the notion of $\\mathfrak{g}$-standard Young tableaux, introduced by Lakshmibai and studied by Littelmann, that provides a combinatorial model for the characters of the irreducible representations of any classical semisimple Lie algebra $\\mathfrak{g}$. We construct a new version of these objects, which differs from the old one for $\\mathfrak{g} = \\mathfrak{so}(2r)$ and seems, in some sense, simpler and more natural.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-25T15:02:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B20",
      "22E46",
      "22E47"
    ],
    "keywords": [
      "levi subgroup",
      "representations",
      "semisimple real lie algebra",
      "classical semisimple lie algebra",
      "maximal split torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}