{
  "id": "2107.00170",
  "version": "v1",
  "published": "2021-07-01T01:39:41.000Z",
  "updated": "2021-07-01T01:39:41.000Z",
  "title": "A new tableau model for irreducible polynomial representations of the orthogonal group",
  "authors": [
    "Hideya Watanabe"
  ],
  "comment": "37 pages",
  "categories": [
    "math.CO",
    "math.QA",
    "math.RT"
  ],
  "abstract": "We provide a new tableau model from which one can easily deduce the characters of irreducible polynomial representations of the orthogonal group $\\mathrm{O}_n(\\mathbb{C})$. This model originates from representation theory of the $\\imath$quantum group of type AI, and is equipped with a combinatorial structure, which we call AI-crystal structure. This structure enables us to describe combinatorially the tensor product of an $\\mathrm{O}_n(\\mathbb{C})$-module and a $\\mathrm{GL}_n(\\mathbb{C})$-module, and the branching from $\\mathrm{GL}_n(\\mathbb{C})$ to $\\mathrm{O}_n(\\mathbb{C})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-01T01:39:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "17B10",
      "17B37"
    ],
    "keywords": [
      "irreducible polynomial representations",
      "tableau model",
      "orthogonal group",
      "model originates",
      "ai-crystal structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}