{
  "id": "1210.1308",
  "version": "v1",
  "published": "2012-10-04T06:20:13.000Z",
  "updated": "2012-10-04T06:20:13.000Z",
  "title": "Knuth relations, tableaux and MV-cycles",
  "authors": [
    "Stéphane Gaussent",
    "Peter Littelmann",
    "An Hoa Nguyen"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We give a geometric interpretation of the Knuth equivalence relations in terms of the affine Gra{\\ss} mann variety. The Young tableaux are seen as sequences of coweights, called galleries. We show that to any gallery corresponds a Mirkovi\\'c-Vilonen cycle and that two galleries are equivalent if, and only if, their associated MV cycles are equal. Words are naturally identified to some galleries. So, as a corollary, we obtain that two words are Knuth equivalent if, and only if, their associated MV cycles are equal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-04T06:20:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "knuth relations",
      "associated mv cycles",
      "knuth equivalence relations",
      "geometric interpretation",
      "mann variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.1308G"
    }
  }
}