{
  "id": "1505.04800",
  "version": "v1",
  "published": "2015-05-18T20:03:37.000Z",
  "updated": "2015-05-18T20:03:37.000Z",
  "title": "On the structure of Specht modules in the principal block of $FΣ_{3p}$",
  "authors": [
    "Michael Rosas"
  ],
  "comment": "22 pages, manuscript has been submitted to Elsevier",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $F$ be a field of characteristic $p$ at least 5. We study the Loewy structures of Specht modules in the principal block of $F\\Sigma_{3p}$. We show that a Specht module in the block has Loewy length at most 4 and composition length at most 14. Furthermore, we classify which Specht modules have Loewy length 1 or 4, produce a Specht module having 14 composition factors, describe the second radical layer of certain reducible Specht modules, and prove that if a Specht module corresponds to a partition that is $p$-regular and $p$-restricted then the head of the Specht module does not extend the socle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-18T20:03:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principal block",
      "loewy length",
      "specht module corresponds",
      "composition length",
      "composition factors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150504800R"
    }
  }
}