{
  "id": "1811.10472",
  "version": "v1",
  "published": "2018-11-26T16:06:49.000Z",
  "updated": "2018-11-26T16:06:49.000Z",
  "title": "On a converse theorem for $G_2$ over finite fields",
  "authors": [
    "Baiying Liu",
    "Qing Zhang"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper, we prove certain multiplicity one theorems and define twisted gamma factors for irreducible generic cuspidal representations of split $G_2$ over finite fields $k$ of odd characteristic. Then we prove the first converse theorem for exceptional groups, namely, $GL_1$ and $GL_2$-twisted gamma factors will uniquely determine an irreducible generic cuspidal representation of $G_2(k)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-26T16:06:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite fields",
      "irreducible generic cuspidal representation",
      "first converse theorem",
      "define twisted gamma factors",
      "exceptional groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}