On uniform lattices in real semisimple groups

摘要

In this article we prove that the co-compactness of the arithmetic latticesin a connected semisimple real Lie group is preserved if the lattices underconsideration are representation equivalent. This is in the spirit of thequestion posed by Gopal Prasad and A. S. Rapinchuk where instead ofrepresentation equivalence, the lattices under consideration are weaklycommensurable Zariski dense subgroups.