{
  "id": "0709.4215",
  "version": "v1",
  "published": "2007-09-26T17:15:46.000Z",
  "updated": "2007-09-26T17:15:46.000Z",
  "title": "Multiplicity one Theorems",
  "authors": [
    "Avraham Aizenbud",
    "Dmitry Gourevitch",
    "Steve Rallis",
    "Gérard Schiffmann"
  ],
  "comment": "A synthesis, with some simplified proofs, of arXiv:0705.2168v1 and arXiv:0707.2363v2",
  "journal": "Annals of Mathematics, Vol. 172 (2010), No. 2, 1407-1434",
  "categories": [
    "math.RT"
  ],
  "abstract": "In the local, characteristic 0, non archimedean case, we consider distributions on GL(n+1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by transposition. This implies that an admissible irreducible representation of GL(n+1), when restricted to GL(n) decomposes with multiplicity one. Similar Theorems are obtained for orthogonal or unitary groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-26T17:15:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiplicity",
      "non archimedean case",
      "distributions",
      "adjoint action",
      "unitary groups"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.4215A"
    }
  }
}