{
  "id": "1409.1305",
  "version": "v1",
  "published": "2014-09-04T02:36:00.000Z",
  "updated": "2014-09-04T02:36:00.000Z",
  "title": "A superdimension formula for gl(m|n) modules",
  "authors": [
    "Michael Chmutov",
    "Rachel Karpman",
    "Shifra Reif"
  ],
  "comment": "6 pages, no figures",
  "categories": [
    "math.RT",
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We give a formula for the superdimension of a finite-dimensional simple gl(m|n)-module using the Su-Zhang character formula. As a corollary, we obtain a simple algebraic proof of a conjecture of Kac-Wakimoto for gl(m|n), namely, a simple module has nonzero superdimension if and only if it has maximal degree of atypicality. This conjecture was proven originally by Serganova using the Duflo-Serganova associated variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-04T02:36:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "superdimension formula",
      "simple algebraic proof",
      "su-zhang character formula",
      "conjecture",
      "simple module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.1305C"
    }
  }
}