{
  "id": "2309.00294",
  "version": "v1",
  "published": "2023-09-01T06:59:57.000Z",
  "updated": "2023-09-01T06:59:57.000Z",
  "title": "On representation equivalence and multiplicity measure for lattices in Lie Groups",
  "authors": [
    "Chandrasheel Bhagwat",
    "Kaustabh Mondal"
  ],
  "comment": "15 Pages",
  "categories": [
    "math.RT",
    "math.GR",
    "math.NT"
  ],
  "abstract": "We prove an analogue of the strong multiplicity one theorem in the context of finite covolume lattices in the group $G ={ \\rm SO}(2,1)^\\circ$. We show that the multiplicity measures of two lattices are same if they agree outside a finite measure subset of $\\widehat G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-01T06:59:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40",
      "22E45",
      "53C35"
    ],
    "keywords": [
      "multiplicity measure",
      "representation equivalence",
      "lie groups",
      "finite covolume lattices",
      "finite measure subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}