{
  "id": "0708.2941",
  "version": "v2",
  "published": "2007-08-22T15:04:10.000Z",
  "updated": "2008-03-11T18:24:59.000Z",
  "title": "Hook modules for general linear groups",
  "authors": [
    "Stephen Doty",
    "Stuart Martin"
  ],
  "comment": "10 pages",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "For an arbitrary infinite field k of characteristic p > 0, we describe the structure of a block of the algebraic monoid M_n(k) (all n x n matrices over k), or, equivalently, a block of the Schur algebra S(n,p), whose simple modules are indexed by p-hook partitions. The result is known; we give an elementary and self-contained proof, based only on a result of Peel and Donkin's description of the blocks of Schur algebras. The result leads to a character formula for certain simple GL_n(k)-modules, valid for all n and all p. This character formula is a special case of one found by Brundan, Kleshchev, and Suprunenko and, independently, by Mathieu and Papadopoulo.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-03-11T18:24:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general linear groups",
      "hook modules",
      "character formula",
      "schur algebra",
      "arbitrary infinite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.2941D"
    }
  }
}