{
  "id": "1902.03843",
  "version": "v1",
  "published": "2019-02-11T12:33:31.000Z",
  "updated": "2019-02-11T12:33:31.000Z",
  "title": "A Sundaram type bijection for $\\mathrm{SO}(2k+1)$: vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau",
  "authors": [
    "Judith Jagenteufel"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We present a bijection between vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau for the special orthogonal group $\\mathrm{SO}(2k+1)$. This bijection is motivated by the direct-sum-decomposition of the $r$th tensor power of the defining representation of $\\mathrm{SO}(2k+1)$. To formulate it, we use Kwon's orthogonal Littlewood-Richardson tableaux and introduce new alternative tableaux they are in bijection with. Moreover we use a suitably defined descent set for vacillating tableaux to determine the quasi-symmetric expansion of the Frobenius characters of the isotypic components.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-11T12:33:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10"
    ],
    "keywords": [
      "standard young tableau",
      "sundaram type bijection",
      "vacillating tableaux",
      "pairs consisting",
      "kwons orthogonal littlewood-richardson tableaux"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}