{
  "id": "0710.0253",
  "version": "v1",
  "published": "2007-10-01T10:13:18.000Z",
  "updated": "2007-10-01T10:13:18.000Z",
  "title": "Crystal graphs for general linear Lie superalgebras and quasi-symmetric functions",
  "authors": [
    "Jae-Hoon Kwon"
  ],
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We give a new representation theoretic interpretation of the ring of quasi-symmetric functions. This is obtained by showing that the super analogue of the Gessel's fundamental quasi-symmetric function can be realized as the character of an irreducible crystal for the Lie superalgebra $\\frak{gl}_{n|n}$ associated to its non-standard Borel subalgebra with a maximal number of odd isotropic simple roots. We also present an algebraic characterization of these super quasi-symmetric functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-01T10:13:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37"
    ],
    "keywords": [
      "general linear lie superalgebras",
      "crystal graphs",
      "gessels fundamental quasi-symmetric function",
      "odd isotropic simple roots",
      "super quasi-symmetric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.0253K"
    }
  }
}