{
  "id": "1304.2868",
  "version": "v1",
  "published": "2013-04-10T07:41:22.000Z",
  "updated": "2013-04-10T07:41:22.000Z",
  "title": "Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups",
  "authors": [
    "Birgit Speh",
    "Genkai Zhang"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We consider the spherical complementary series of rank one Lie groups $H_n=\\SO_0(n, 1; \\mathbb F)$ for $\\mathbb F=\\mathbb R, \\mathbb C, \\mathbb H$. We prove that there exist finitely many discrete components in its restriction under the subgroup $H_{n-1}=\\SO_0(n-1, 1; \\mathbb F)$. This is proved by imbedding the complementary series into analytic continuation of holomorphic discrete series of $G_n=SU(n, 1)$, $SU(n, 1)\\times SU(n, 1)$ and $SU(2n, 2)$ and by the branching of holomorphic representations under the corresponding subgroup $G_{n-1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-10T07:41:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semisimple lie groups",
      "unitary representations",
      "symmetric subgroups",
      "restriction",
      "holomorphic discrete series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.2868S"
    }
  }
}