{
  "id": "2208.11763",
  "version": "v1",
  "published": "2022-08-24T20:34:54.000Z",
  "updated": "2022-08-24T20:34:54.000Z",
  "title": "On Poisson transform for spinors",
  "authors": [
    "Salem Bensaïd",
    "Abdelhamid Boussejra",
    "Khalid Koufany"
  ],
  "categories": [
    "math.RT",
    "math.FA"
  ],
  "abstract": "Let $(\\tau,V_\\tau)$ be a spinor representation of $\\mathrm{Spin}(n)$ and let $(\\sigma,V_\\sigma)$ be a spinor representation of $\\mathrm{Spin}(n-1)$ that occurs in the restriction $\\tau_{\\mid \\mathrm{Spin}(n-1)}$. We consider the real hyperbolic space $H^n(\\mathbb R)$ as the rank one homogeneous space $\\mathrm{Spin}_0(1,n)/\\mathrm{Spin}(n)$ and the spinor bundle $\\Sigma H^n(\\mathbb R)$ over $H^n(\\mathbb R)$ as the homogeneous bundle $\\mathrm{Spin}_0(1,n)\\times_{\\mathrm{Spin}(n)} V_\\tau$. Our aim is to characterize eigenspinors of the algebra of invariant differential operators acting on $\\Sigma H^n(\\mathbb R)$ which can be written as the Poisson transform of $L^p$-sections of the bundle $\\mathrm{Spin}(n)\\times_{\\mathrm{Spin}(n-1)} V_\\sigma$ over the boundary $S^{n-1}\\simeq \\mathrm{Spin}(n)/\\mathrm{Spin}(n-1)$ of $H^n(\\mathbb R)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-24T20:34:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58A10",
      "43A85",
      "53C35",
      "22E30"
    ],
    "keywords": [
      "poisson transform",
      "spinor representation",
      "real hyperbolic space",
      "spinor bundle",
      "invariant differential operators acting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}