• On the set of discrete subgroups of bounded covolume in a semisimple group

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      https://www.ias.ac.in/article/fulltext/pmsc/097/01-03/0045-0052

    • Keywords

       

      Discrete subgroups; bounded covolume; semisimple group

    • Abstract

       

      In this noteG is a locally compact group which is the product of finitely many groups Gs(ks)(s∈S), where ks is a local field of characteristic zero and Gs an absolutely almost simpleks-group, ofks-rank ≥1. We assume that the sum of the rs is ≥2 and fix a Haar measure onG. Then, given a constantc > 0, it is shown that, up to conjugacy,G contains only finitely many irreducible discrete subgroupsL of covolume ≥c (4.2). This generalizes a theorem of H C Wang for real groups. His argument extends to the present case, once it is shown thatL is finitely presented (2.4) and locally rigid (3.2).

    • Author Affiliations

       

      A Borel1

      1. School of Mathematics, The Institute for Advanced Study, Princeton, New Jersey - 08540, USA
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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