{
  "id": "0909.2999",
  "version": "v1",
  "published": "2009-09-16T12:32:17.000Z",
  "updated": "2009-09-16T12:32:17.000Z",
  "title": "Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups",
  "authors": [
    "Wee Teck Gan",
    "Benedict H. Gross",
    "Dipendra Prasad"
  ],
  "comment": "112 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We consider several questions about restriction of representations of classical and metaplectic groups over local and global fields to subgroups, extending considerably the scope of the earlier work on $SO(n),SO(n-1)$. This includes Bessel and Fourier-Jacobi models too. We formulate several conjectures about these restriction problems involving root numbers of symplectic representations in the local case, and central critical L-value in the global case. Along the way we prove several results both in number theory and representation theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-16T12:32:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11F70"
    ],
    "keywords": [
      "symplectic local root numbers",
      "central critical l-value",
      "restriction problems",
      "representation theory",
      "classical groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 112,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.2999T"
    }
  }
}