{
  "id": "0806.4031",
  "version": "v1",
  "published": "2008-06-25T06:08:19.000Z",
  "updated": "2008-06-25T06:08:19.000Z",
  "title": "On Unitary Representations of GL2n Distinguished by the Symplectic Group",
  "authors": [
    "Omer Offen",
    "Eitan Sayag"
  ],
  "comment": "Two references added and minor editing of the published version",
  "journal": "Journal of Number Theory No.125, 2007",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "We provide a family of representations of GL(2n) over a p-adic field that admit a non-vanishing linear functional invariant under the symplectic group (i.e. representations that are Sp(2n)- distinguished). While our result generalizes a result of M. Heumos and S. Rallis our methods, unlike their purely local technique, re- lies on the theory of automorphic forms. The results of this paper together with later works by the authors imply that the family of representations studied in this paper contains all irreducible, unitary representations of the general linear group that are distin- guished by the symplectic group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-25T06:08:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symplectic group",
      "unitary representations",
      "general linear group",
      "non-vanishing linear functional invariant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.4031O"
    }
  }
}