{
  "id": "2312.14296",
  "version": "v1",
  "published": "2023-12-21T21:01:38.000Z",
  "updated": "2023-12-21T21:01:38.000Z",
  "title": "Strong Property $(T)$ and relatively hyperbolic groups",
  "authors": [
    "Hermès Lajoinie-Dodel"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.GR",
    "math.GT",
    "math.MG"
  ],
  "abstract": "We prove that relatively hyperbolic groups do not have Lafforgue strong Property $(T)$ with respect to Hilbert spaces. To do so we construct an unbounded affine representation of such groups, whose linear part is of polynomial growth of degree $2$. Moreover, this representation is proper for the metric of the coned-off graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-21T21:01:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C24",
      "20F65",
      "20F67",
      "19J35"
    ],
    "keywords": [
      "relatively hyperbolic groups",
      "lafforgue strong property",
      "hilbert spaces",
      "unbounded affine representation",
      "linear part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}