{
  "id": "0705.4330",
  "version": "v3",
  "published": "2007-05-30T03:03:30.000Z",
  "updated": "2007-11-13T20:53:39.000Z",
  "title": "Almost-minimal nonuniform lattices of higher rank",
  "authors": [
    "Vladimir Chernousov",
    "Lucy Lifschitz",
    "Dave Witte Morris"
  ],
  "comment": "23 pages. Minor corrections, and added remarks about which of the subgroups we construct are simply connected",
  "categories": [
    "math.GR",
    "math.DG",
    "math.RT"
  ],
  "abstract": "If Gamma is a nonuniform, irreducible lattice in a semisimple Lie group whose real rank is greater than 1, we show Gamma contains a subgroup that is isomorphic to a nonuniform, irreducible lattice in either SL(3,R), SL(3,C), or a direct product SL(2,R)^m x SL(2,C)^n$, with m + n > 1. (In geometric terms, this can be interpreted as a statement about the existence of totally geodesic subspaces of finite-volume, noncompact, locally symmetric spaces of higher rank.) Another formulation of the result states that if G is any isotropic, almost simple algebraic group over Q (the rational numbers), such that the real rank of G is greater than 1, then G contains an isotropic, almost simple Q-subgroup H, such that H is quasisplit, and the real rank of H is greater than 1.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-11-13T20:53:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40",
      "20G30",
      "53C35"
    ],
    "keywords": [
      "almost-minimal nonuniform lattices",
      "higher rank",
      "real rank",
      "semisimple lie group",
      "irreducible lattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.4330C"
    }
  }
}