{
  "id": "1608.04502",
  "version": "v1",
  "published": "2016-08-16T07:09:08.000Z",
  "updated": "2016-08-16T07:09:08.000Z",
  "title": "Irreducible projective representations of the symmetric group which remain irreducible in characteristic $2$",
  "authors": [
    "Matthew Fayers"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "For any finite group $G$ and any prime $p$ one can ask which ordinary irreducible representations remain irreducible in characteristic $p$. We answer this question for $p=2$ when $G$ is a proper double cover of the symmetric group. Our techniques involve constructing part of the decomposition matrix for a Rouquier block of a double cover, restricting to subgroups using the Brundan--Kleshchev modular branching rules and comparing the dimensions of irreducible representations via the bar-length formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-16T07:09:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "20C25",
      "05E10"
    ],
    "keywords": [
      "symmetric group",
      "irreducible projective representations",
      "characteristic",
      "irreducible representations remain irreducible",
      "ordinary irreducible representations remain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}