On uniform lattices in real semisimple groups

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

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