{
  "id": "1303.5850",
  "version": "v2",
  "published": "2013-03-23T14:43:14.000Z",
  "updated": "2013-09-28T21:14:20.000Z",
  "title": "Descent sets for symplectic groups",
  "authors": [
    "Martin Rubey",
    "Bruce Sagan",
    "Bruce W. Westbury"
  ],
  "comment": "22 pages, 2 figures",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "The descent set of an oscillating (or up-down) tableau is introduced. This descent set plays the same role in the representation theory of the symplectic groups as the descent set of a standard tableau plays in the representation theory of the general linear groups. In particular, we show that the descent set is preserved by Sundaram's correspondence. This gives a direct combinatorial interpretation of the branching rules for the defining representations of the symplectic groups; equivalently, for the Frobenius character of the action of a symmetric group on an isotypic subspace in a tensor power of the defining representation of a symplectic group.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-28T21:14:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05E10",
      "20C15"
    ],
    "keywords": [
      "symplectic group",
      "representation theory",
      "defining representation",
      "standard tableau plays",
      "general linear groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.5850R"
    }
  }
}