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

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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 simplek s-group, ofk s-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).

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

    A. Borel

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Borel, A. On the set of discrete subgroups of bounded covolume in a semisimple group. Proc. Indian Acad. Sci. (Math. Sci.) 97, 45–52 (1987). https://doi.org/10.1007/BF02837812

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