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Divergent torus orbits in homogeneous spaces of ℚ-rank two

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Abstract

LetG be a semisimple algebraic ℚ-group, let Γ be an arithmetic subgroup ofG, and letT be an ℝ-split torus inG. We prove that if there is a divergentT ℝ-orbit in Γ\G ℝ, and ℚ-rankG≤2, then dimT≤ℚ-rankG. This provides a partial answer to a question of G. Tomanov and B. Weiss.

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Authors and Affiliations

  1. Department of Mathematics, Oklahoma State University, 74078, Stillwater, OK, USA

    Pralay Chatterjee

  2. Mathematics Department, Rice University, 77005, Houston, TX, USA

    Pralay Chatterjee

  3. Department of Mathematics, Oklahoma State University, 74078, Stillwater, OK, USA

    Dave Witte Morris

  4. Department of Mathematics and Computer Science, University of Lethbridge, T1K 3M4, Lethbridge, AB, Canada

    Dave Witte Morris

Authors
  1. Pralay Chatterjee
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  2. Dave Witte Morris
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Correspondence to Pralay Chatterjee.

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Chatterjee, P., Morris, D.W. Divergent torus orbits in homogeneous spaces of ℚ-rank two. Isr. J. Math. 152, 229–243 (2006). https://doi.org/10.1007/BF02771985

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  • DOI: https://doi.org/10.1007/BF02771985

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