{
  "id": "1607.01982",
  "version": "v1",
  "published": "2016-07-07T12:16:59.000Z",
  "updated": "2016-07-07T12:16:59.000Z",
  "title": "Gamma factors root numbers and distinction",
  "authors": [
    "Nadir Matringe",
    "Omer Offen"
  ],
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "We study a relation between distinction and special values of local invariants for representations of the general linear group over a quadratic extension of $p$-adic fields. We show that the local Rankin-Selberg root number of any pair of distinguished representation is trivial and as a corollary we obtain an analogue for the global root number of any pair of distinguished cuspidal representations. We further study the extent to which the gamma factor at $1/2$ is trivial for distinguished representations as well as the converse problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-07T12:16:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11F70"
    ],
    "keywords": [
      "gamma factors root numbers",
      "distinction",
      "local rankin-selberg root number",
      "distinguished representation",
      "general linear group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}