{
  "id": "1602.02168",
  "version": "v1",
  "published": "2016-02-05T21:23:52.000Z",
  "updated": "2016-02-05T21:23:52.000Z",
  "title": "Dimensions of the irreducible representations of the symmetric and alternating group",
  "authors": [
    "Korneel Debaene"
  ],
  "comment": "24 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We establish the existence of an irreducible representation of $A_n$ whose dimension does not occur as the dimension of an irreducible representation of $S_n$, and vice versa. This proves a conjecture by Tong-Viet. The main ingredient in the proof is a result on large prime factors in short intervals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-05T21:23:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "20C40"
    ],
    "keywords": [
      "irreducible representation",
      "alternating group",
      "large prime factors",
      "short intervals",
      "main ingredient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}