{
  "id": "2010.01026",
  "version": "v1",
  "published": "2020-10-02T14:29:53.000Z",
  "updated": "2020-10-02T14:29:53.000Z",
  "title": "Restriction of irreducible unitary representations of Spin(N,1) to parabolic subgroups",
  "authors": [
    "Gang Liu",
    "Yoshiki Oshima",
    "Jun Yu"
  ],
  "comment": "61 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper, we obtain explicit branching laws for all unitary representations of $\\operatorname{Spin}(N,1)$ restricted to a parabolic subgroup $P$. The restriction turns out to be a finite direct sum of irreducible unitary representations of $P$. We also verify Duflo's conjecture for the branching law of tempered representations of $\\operatorname{Spin}(N,1)$ with respect to a minimal parabolic subgroup $P$. That is to show: in the framework of orbit method, the branching law of a tempered representation is determined by the behavior of the moment map from the corresponding coadjoint orbit. A few key tools used in this work include: Fourier transform, Knapp-Stein intertwining operators, Casselman-Wallach globalization, Zuckerman translation principle, du Cloux's result of smooth representations for semi-algebraic groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-02T14:29:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46"
    ],
    "keywords": [
      "irreducible unitary representations",
      "branching law",
      "zuckerman translation principle",
      "minimal parabolic subgroup",
      "tempered representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}