{
  "id": "1306.1033",
  "version": "v3",
  "published": "2013-06-05T09:38:25.000Z",
  "updated": "2014-07-30T12:21:33.000Z",
  "title": "The irreducible representations of the alternating group which remain irreducible in characteristic p",
  "authors": [
    "Matthew Fayers"
  ],
  "comment": "Accepted for publication in Transactions of the American Mathematical Society. Many thanks to the referee",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let p be an odd prime, and A_n the alternating group of degree n. We determine which ordinary irreducible representations of A_n remain irreducible in characteristic p, verifying the author's conjecture from [Represent. Theory 14, 601-626]. Given the preparatory work done in [op. cit.], our task is to determine which self-conjugate partitions label Specht modules for the symmetric group in characteristic p having exactly two composition factors. This is accomplished through the use of the Robinson-Brundan-Kleshchev 'i-restriction' functors, together with known results on decomposition numbers for the symmetric group and additional results on the Mullineux map and homomorphisms between Specht modules.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-30T12:21:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "05E10",
      "20C20"
    ],
    "keywords": [
      "irreducible representations",
      "alternating group",
      "remain irreducible",
      "characteristic",
      "self-conjugate partitions label specht modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.1033F"
    }
  }
}