{
  "id": "math/0610644",
  "version": "v3",
  "published": "2006-10-21T11:20:06.000Z",
  "updated": "2007-10-20T14:17:24.000Z",
  "title": "The Character of the Weil Representation",
  "authors": [
    "Teruji Thomas"
  ],
  "comment": "19 pages, accepted to appear in the Journal of the LMS. This final arXiv version is pre-proof",
  "journal": "J. LMS. (2) 77 (2008), 221-239",
  "doi": "10.1112/jlms/jdm098",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let V be a symplectic vector space over a finite or local field. We compute the character of the Weil representation of the metaplectic group Mp(V). The final formulas are overtly free of choices (e.g. they do not involve the usual choice of a Lagrangian subspace of V). Along the way, in results similar to those of K. Maktouf, we relate the character to the Weil index of a certain quadratic form, which may be understood as a Maslov index. This relation also expresses the character as the pullback of a certain simple function from Mp(V\\oplus V).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-10-20T14:17:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F27"
    ],
    "keywords": [
      "weil representation",
      "symplectic vector space",
      "metaplectic group mp",
      "local field",
      "simple function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10644T"
    }
  }
}