{
  "id": "1808.08255",
  "version": "v1",
  "published": "2018-08-24T18:18:55.000Z",
  "updated": "2018-08-24T18:18:55.000Z",
  "title": "Supersingular representations of rank 1 groups",
  "authors": [
    "Karol Koziol"
  ],
  "comment": "6 pages. Comments welcome!",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "We prove that any connected reductive group of semisimple $F$-rank 1 over a $p$-adic field admits an irreducible admissible supersingular mod-$p$ representation. This establishes one of the missing cases in Vign\\'eras' existence proof for general reductive groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-24T18:18:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supersingular representations",
      "adic field admits",
      "existence proof",
      "general reductive groups",
      "irreducible admissible supersingular"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}