{
  "id": "1104.4827",
  "version": "v2",
  "published": "2011-04-26T00:24:25.000Z",
  "updated": "2016-10-10T16:20:57.000Z",
  "title": "Irreducibility of automorphic Galois representations of GL(n), n at most 5",
  "authors": [
    "Frank Calegari",
    "Toby Gee"
  ],
  "comment": "Erratum: there is a gap in the proof of the main theorem for n=4, 5",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let pi be a regular, algebraic, essentially self-dual cuspidal automorphic representation of GL_n(A_F), where F is a totally real field and n is at most 5. We show that for all primes l, the l-adic Galois representations associated to pi are irreducible, and for all but finitely many primes l, the mod l Galois representations associated to pi are also irreducible. We also show that the Lie algebras of the Zariski closures of the l-adic representations are independent of l.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-26T00:24:25.000Z",
      "comment": "18 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-10-10T16:20:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F33"
    ],
    "keywords": [
      "automorphic galois representations",
      "essentially self-dual cuspidal automorphic representation",
      "irreducibility",
      "l-adic galois representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4827C"
    }
  }
}