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Jan 13, 2013 at 12:31 comment added Venkataramana Apologies: in this case, superrigidity and complete reducibility follow from the congruence subgroup property. Complete reducibility does not follow directly from super-rigidity but one has to have an extra argument using vanishing of the first cohomology of $\Gamma $ with values in finite dimensional representations. This is also done in Margulis' book on discrete subgroups of semi-simple Lie groups.
Jan 13, 2013 at 12:22 history answered Venkataramana CC BY-SA 3.0