{
  "id": "2307.06791",
  "version": "v1",
  "published": "2023-07-13T15:00:06.000Z",
  "updated": "2023-07-13T15:00:06.000Z",
  "title": "Maximal representations in lattices of the symplectic group",
  "authors": [
    "Jacques Audibert"
  ],
  "comment": "17 pages, comments are welcome",
  "categories": [
    "math.GT",
    "math.GR",
    "math.NT"
  ],
  "abstract": "We prove that all lattices of Sp(2n,R), except those commensurable with Sp(4k+2,Z) when n=2k+1, contain the image of infinitely many mapping class group orbits of Zariski-dense maximal representation that are continuous deformations of maximal diagonal representations. In particular, we show that Sp(4k,Z) contain Zariski-dense surface subgroups for all k.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-13T15:00:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40"
    ],
    "keywords": [
      "symplectic group",
      "contain zariski-dense surface subgroups",
      "mapping class group orbits",
      "zariski-dense maximal representation",
      "maximal diagonal representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}