{
  "id": "math/0403110",
  "version": "v1",
  "published": "2004-03-05T18:32:02.000Z",
  "updated": "2004-03-05T18:32:02.000Z",
  "title": "Properties of some character tables related to the symmetric groups",
  "authors": [
    "Christine Bessenrodt",
    "Jorn B. Olsson",
    "Richard P. Stanley"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We determine invariants like the Smith normal form and the determinant for certain integral matrices which arise from the character tables of the symmetric groups S_n and their double covers. In particular, we give a simple computation, based on the theory of Hall-Littlewood symmetric functions, of the determinant of the regular character table of S_n with respect to an integer r>1. This result had earlier been proved by Olsson in a longer and more indirect manner. As a consequence, we obtain a new proof of the Mathas' Conjecture on the determinant of the Cartan matrix of the Iwahori-Hecke algebra. When r is prime we determine the Smith normal form of the regular character table. Taking r large yields the Smith normal form of the full character table of S_n. Analogous results are then given for spin characters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-03-05T18:32:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "20C30"
    ],
    "keywords": [
      "symmetric groups",
      "character tables",
      "smith normal form",
      "regular character table",
      "properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3110B"
    }
  }
}