{
  "id": "0908.3035",
  "version": "v4",
  "published": "2009-08-20T23:50:33.000Z",
  "updated": "2023-05-06T11:14:21.000Z",
  "title": "Some simple modules for classical groups and $p$-ranks of orthogonal and Hermitian geometries",
  "authors": [
    "Ogul Arslan",
    "Peter Sin"
  ],
  "comment": "33 pages, corrected inequality in statement of Thm 1.8 from $n-2\\le up\\le p+n-3$ to $n-2\\le up\\le p+n-4$",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We determine the characters of the simple composition factors and the submodule lattices of certain Weyl modules for classical groups. The results have several applications. The simple modules arise in the study of incidence systems in finite geometries and knowledge of their dimensions yields the $p$-ranks of these incidence systems.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-13T12:34:21.000Z",
      "comment": "33 pages, corrected parity of u in statement of Theorem 1.6(b)",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2023-05-06T11:14:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "05E10"
    ],
    "keywords": [
      "classical groups",
      "hermitian geometries",
      "orthogonal",
      "incidence systems",
      "simple composition factors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.3035A"
    }
  }
}