{
  "id": "1511.00668",
  "version": "v1",
  "published": "2015-11-02T20:41:37.000Z",
  "updated": "2015-11-02T20:41:37.000Z",
  "title": "The Standard Representation of the Symmetric Group $S_n$ over the Ring of Integers",
  "authors": [
    "Kunle Adegoke",
    "Olawanle Layeni",
    "Rauf Giwa",
    "Gbenga Olunloyo"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this paper we give a Casimir Invariant for the Symmetric group $S_n$. Furthermore we obtain and present, for the first time in the literature, explicit formulas for the matrices of the standard representation in terms of the matrices of the permutation representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-02T20:41:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30"
    ],
    "keywords": [
      "symmetric group",
      "standard representation",
      "permutation representation",
      "explicit formulas",
      "casimir invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}