{
  "id": "0907.0811",
  "version": "v1",
  "published": "2009-07-04T23:03:32.000Z",
  "updated": "2009-07-04T23:03:32.000Z",
  "title": "Vertices of Specht modules and blocks of the symmetric group",
  "authors": [
    "Mark Wildon"
  ],
  "comment": "18 pages, 1 figure",
  "categories": [
    "math.RT"
  ],
  "abstract": "This paper studies the vertices, in the sense defined by J. A. Green, of Specht modules for symmetric groups. The main theorem gives, for each indecomposable non-projective Specht module, a large subgroup contained in one of its vertices. A corollary of this theorem is a new way to determine the defect groups of symmetric groups. We also use it to find the Green correspondents of a particular family of simple Specht modules; as a corollary, we get a new proof of the Brauer correspondence for blocks of the symmetric group. The proof of the main theorem uses the Brauer homomorphism on modules, as developed by M. Brou{\\'e}, together with combinatorial arguments using Young tableaux.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-04T23:03:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "20C20"
    ],
    "keywords": [
      "symmetric group",
      "main theorem",
      "simple specht modules",
      "defect groups",
      "large subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.0811W"
    }
  }
}