{
  "id": "1010.0463",
  "version": "v2",
  "published": "2010-10-04T01:53:16.000Z",
  "updated": "2010-10-09T07:29:30.000Z",
  "title": "Combinatorial bases for covariant representations of the Lie superalgebra gl(m|n)",
  "authors": [
    "A. I. Molev"
  ],
  "comment": "40 pages, minor corrections made",
  "journal": "Bulletin of the Institute of Mathematics, Academia Sinica 6 (2011), 415-462",
  "categories": [
    "math.RT",
    "math.CO",
    "math.QA"
  ],
  "abstract": "Covariant tensor representations of gl(m|n) occur as irreducible components of tensor powers of the natural (m+n)-dimensional representation. We construct a basis of each covariant representation and give explicit formulas for the action of the generators of gl(m|n) in this basis. The basis has the property that the natural Lie subalgebras gl(m) and gl(n) act by the classical Gelfand-Tsetlin formulas. The main role in the construction is played by the fact that the subspace of gl(m)-highest vectors in any finite-dimensional irreducible representation of gl(m|n) carries a structure of an irreducible module over the Yangian Y(gl(n)). One consequence is a new proof of the character formula for the covariant representations first found by Berele and Regev and by Sergeev.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-09T07:29:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie superalgebra",
      "combinatorial bases",
      "natural lie subalgebras gl",
      "covariant representations first",
      "covariant tensor representations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 871944,
      "adsabs": "2010arXiv1010.0463M"
    }
  }
}