{
  "id": "1712.05552",
  "version": "v1",
  "published": "2017-12-15T06:15:52.000Z",
  "updated": "2017-12-15T06:15:52.000Z",
  "title": "Unipotent representations of real classical groups",
  "authors": [
    "Jia-jun Ma",
    "Binyong Sun",
    "Chen-Bo Zhu"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathbf G$ be a complex orthogonal or complex symplectic group, and let $G$ be a real form of $\\mathbf G$, namely $G$ is a real orthogonal group, a real symplectic group, a quaternionic orthogonal group, or a quaternionic symplectic group. For a fixed parity $\\mathbb p\\in \\mathbb Z/2\\mathbb Z$, we define a set $\\mathrm{Nil}^{\\mathbb p}_{\\mathbf G}(\\mathfrak g)$ of nilpotent $\\mathbf G$-orbits in $\\mathfrak g$ (the Lie algebra of $\\mathbf G$). When $\\mathbb p$ is the parity of the dimension of the standard module of $\\mathbf G$, this is the set of the stably trivial special nilpotent orbits, which includes all rigid special nilpotent orbits. For each $\\mathcal O \\in \\mathrm{Nil}^{\\mathbb p}_{\\mathbf G}(\\mathfrak g)$, we construct all unipotent representations of $G$ (or its metaplectic cover when $G$ is a real symplectic group and $\\mathbb p$ is odd) attached to $\\mathcal O$ via the method of theta lifting and show in particular that they are unitary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-15T06:15:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E45",
      "22E46"
    ],
    "keywords": [
      "real classical groups",
      "unipotent representations",
      "real symplectic group",
      "stably trivial special nilpotent orbits",
      "orthogonal group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}