{
  "id": "0903.1417",
  "version": "v3",
  "published": "2009-03-08T12:44:54.000Z",
  "updated": "2012-07-11T11:33:11.000Z",
  "title": "Multiplicity one theorems for Fourier-Jacobi models",
  "authors": [
    "Binyong Sun"
  ],
  "comment": "The matrix in Section 1 is revised, results unchanged. To appear in American Journal of Mathematics",
  "categories": [
    "math.RT"
  ],
  "abstract": "For every genuine irreducible admissible smooth representation $\\pi$ of the metaplectic group $\\widetilde{\\Sp}(2n)$ over a p-adic field, and every smooth oscillator representation $\\omega_\\psi$ of $\\widetilde{\\Sp}(2n)$, we prove that the tensor product $\\pi\\otimes \\omega_\\psi$ is multiplicity free as a smooth representation of the symplectic group $\\Sp(2n)$. Similar results are proved for general linear groups and unitary groups.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-07-11T11:33:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E35",
      "22E46"
    ],
    "keywords": [
      "fourier-jacobi models",
      "multiplicity",
      "smooth oscillator representation",
      "genuine irreducible admissible smooth representation",
      "general linear groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1417S"
    }
  }
}