{
  "id": "2003.02297",
  "version": "v1",
  "published": "2020-03-04T19:19:50.000Z",
  "updated": "2020-03-04T19:19:50.000Z",
  "title": "On unitary representations of algebraic groups over local fields",
  "authors": [
    "Bachir Bekka",
    "Siegfried Echterhoff"
  ],
  "categories": [
    "math.RT",
    "math.GR",
    "math.OA"
  ],
  "abstract": "Let $\\mathbf{G}$ be an algebraic group over a local field $\\mathbf k$ of characteristic zero. We show that the locally compact group $\\mathbf G(\\mathbf k)$ consisting of the $\\mathbf k$-rational points of $\\mathbf G$ is of type I. Moreover, we complete Lipsman's characterization of the groups $\\mathbf G$ for which every irreducible unitary representation of $\\mathbf G(\\mathbf k)$ is a CCR representation and show at the same time that such groups $\\mathbf G(\\mathbf k)$ are trace class as studied recently by Deitmar and van Dijk.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-04T19:19:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D10",
      "22D25",
      "22E50",
      "20G05"
    ],
    "keywords": [
      "algebraic group",
      "local field",
      "complete lipsmans characterization",
      "ccr representation",
      "locally compact group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}