{
  "id": "1801.03780",
  "version": "v1",
  "published": "2018-01-11T14:38:45.000Z",
  "updated": "2018-01-11T14:38:45.000Z",
  "title": "A Sundaram type bijection for $\\mathrm{SO}(3)$: vacillating tableaux and pairs of standard Young tableaux and orthogonal Littlewood-Richardson tableaux",
  "authors": [
    "Judith Braunsteiner"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "Based on the direct-sum-decomposition of the $r^{\\text{th}}$ tensor power of the defining representation of the special orthogonal group $\\mathrm{SO}(2k+1)$ one is interested in a bijective approach for determining the Frobenius characters of the isotypic components. In particular this leads us to a bijection between vacillating tableaux and pairs of standard Young tableaux and orthogonal Littlewood-Richardson tableaux, which we present for $\\mathrm{SO}(3)$. Moreover we introduce the descent set of a vacillating tableau. As our bijection preserves this descent set, we also obtain the quasi-symmetric expansion of the Frobenius characters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-11T14:38:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10"
    ],
    "keywords": [
      "standard young tableaux",
      "orthogonal littlewood-richardson tableaux",
      "sundaram type bijection",
      "vacillating tableaux",
      "descent set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}