{
  "id": "math/0408114",
  "version": "v3",
  "published": "2004-08-09T17:22:51.000Z",
  "updated": "2005-06-13T15:15:10.000Z",
  "title": "The octahedron recurrence and gl(n) crystals",
  "authors": [
    "Andre Henriques",
    "Joel Kamnitzer"
  ],
  "comment": "25 pages, 19 figures, counterexample to Yang-Baxter equation added",
  "categories": [
    "math.CO",
    "math.QA"
  ],
  "abstract": "We study the hive model of gl(n) tensor products, following Knutson, Tao, and Woodward. We define a coboundary category where the tensor product is given by hives and where the associator and commutor are defined using a modified octahedron recurrence. We then prove that this category is equivalent to the category of crystals for the Lie algebra gl(n). The proof of this equivalence uses a new connection between the octahedron recurrence and the Jeu de Taquin and Schutzenberger involution procedures on Young tableaux.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-06-13T15:15:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tensor product",
      "schutzenberger involution procedures",
      "lie algebra gl",
      "young tableaux",
      "coboundary category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8114H"
    }
  }
}