Growth of homogeneous spaces, density of discrete subgroups and Kazhdan's property \((T)\)
It is shown that if \(G\) is a semisimple Lie group with finite center and no compact factors and if \(H\) is a closed unimodular subgroup of \(G\) such that \(G/H\) has subexponential volume growth, then \(H\) is Zariski dense in \(G\). Moreover, if \(G\) has Kazhdan's property \((T)\) then \(G/H\) must have finite volume. The results are extended to semisimple groups over a local field.
scientific article; zbMATH DE number 220746
scientific article