{
  "id": "1112.3127",
  "version": "v1",
  "published": "2011-12-14T06:09:53.000Z",
  "updated": "2011-12-14T06:09:53.000Z",
  "title": "Hooks generate the representation ring of the symmetric group",
  "authors": [
    "Ivan Marin"
  ],
  "comment": "9 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove that the representation ring of the symmetric group on $n$ letters is generated by the exterior powers of its natural $(n-1)$-dimensional representation. The proof we give illustrates a strikingly simple formula due to Y. Dvir. We provide an application and investigate a possible generalization of this result to some other reflection groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-14T06:09:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30"
    ],
    "keywords": [
      "symmetric group",
      "representation ring",
      "hooks generate",
      "strikingly simple formula",
      "exterior powers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.3127M"
    }
  }
}