{
  "id": "1408.4299",
  "version": "v1",
  "published": "2014-08-19T11:28:28.000Z",
  "updated": "2014-08-19T11:28:28.000Z",
  "title": "Gamma Factors of Distinguished Representations of GL_n(C)",
  "authors": [
    "Alexander Kemarsky"
  ],
  "comment": "25 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $(\\pi,V)$ be a $GL_n(\\mathbb{R})$-distinguished, irreducible, admissible representation of $GL_n(\\mathbb{C})$, let $\\pi'$ be an irreducible, admissible, $GL_m(\\mathbb{R})$-distinguished representation of $GL_m(\\mathbb{C})$, and let $\\psi$ be a non-trival character of $\\mathbb{C}$ which is trivial on $\\mathbb{R}$. We prove that Rankin-Selberg gamma factor at $s=\\frac{1}{2}$ is $\\gamma(\\frac{1}{2},\\pi \\times \\pi'; \\psi) = 1$. The result follows as a simple consequence from the characterisation of $GL_n(\\mathbb{R})$-distinguished representations in terms of their Langlands data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-19T11:28:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E45"
    ],
    "keywords": [
      "distinguished representation",
      "rankin-selberg gamma factor",
      "non-trival character",
      "simple consequence",
      "langlands data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.4299K"
    }
  }
}