{
  "id": "0903.2864",
  "version": "v1",
  "published": "2009-03-16T21:54:43.000Z",
  "updated": "2009-03-16T21:54:43.000Z",
  "title": "Multiplicity-free representations of symmetric groups",
  "authors": [
    "Mark Wildon"
  ],
  "comment": "23 pages, 4 figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "Building on work of Saxl, we classify the multiplicity-free permutation characters of all symmetric groups of degree 66 or more. A corollary is a complete list of the irreducible characters of symmetric groups (again of degree 66 or more) which may appear in a multiplicity-free permutation representation. The multiplicity-free characters in a related family of monomial characters are also classified. We end by investigating a consequence of these results for Specht filtrations of permutation modules defined over fields of prime characteristic. Remark: parallel work of Godsil and Meagher (arXiv:math/0612567) gives an independent classification of the multiplicity-free permutation characters of symmetric groups of all degrees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-16T21:54:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "20C20"
    ],
    "keywords": [
      "symmetric groups",
      "multiplicity-free representations",
      "multiplicity-free permutation characters",
      "multiplicity-free permutation representation",
      "independent classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.2864W"
    }
  }
}