{
  "id": "0904.0922",
  "version": "v2",
  "published": "2009-04-06T16:07:49.000Z",
  "updated": "2009-10-02T17:50:00.000Z",
  "title": "Uniqueness of Shalika functionals (the Archimedean case)",
  "authors": [
    "Avraham Aizenbud",
    "Dmitry Gourevitch",
    "Herve Jacquet"
  ],
  "comment": "9 pages. v2:corrected version, to appear in Pacific Journal of Mathematics",
  "journal": "Pacific Journal of Mathematics, 243 no. 2 (2009)",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let F be either R or C. Let $(\\pi,V)$ be an irreducible admissible smooth \\Fre representation of GL(2n,F). A Shalika functional $\\phi:V \\to \\C$ is a continuous linear functional such that for any $g\\in GL_n(F), A \\in \\Mat_{n \\times n}(F)$ and $v\\in V$ we have $$ \\phi[\\pi g & A 0 & g)v] = \\exp(2\\pi i \\re(\\tr (g^{-1}A))) \\phi(v).$$ In this paper we prove that the space of Shalika functionals on V is at most one dimensional. For non-Archimedean F (of characteristic zero) this theorem was proven in [JR].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-02T17:50:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E45"
    ],
    "keywords": [
      "shalika functional",
      "archimedean case",
      "uniqueness",
      "continuous linear functional",
      "characteristic zero"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.0922A"
    }
  }
}