{
  "id": "2406.12626",
  "version": "v1",
  "published": "2024-06-18T13:50:10.000Z",
  "updated": "2024-06-18T13:50:10.000Z",
  "title": "Irreducible representations of $\\mathrm{SL}(2,\\R)$ on Hilbert spaces are admissible",
  "authors": [
    "Francesca Astengo",
    "Michael G. Cowling",
    "Bianca Di Blasio"
  ],
  "comment": "13 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We show that irreducible strongly continuous representations of $\\mathrm{SL}(2,\\mathbb{R})$ on Hilbert spaces are admissible, modulo the recently proposed solution of the invariant subspace problem on Hilbert spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-18T13:50:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert spaces",
      "irreducible representations",
      "admissible",
      "invariant subspace problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}