Cohomology of discrete subgroups of Sp(p,q) (Q917720)

Let G be a connected semisimple Lie group with finite center and no compact factors, let \(\Gamma\) be a uniform discrete subgroup of G and (\(\rho\),F) be a finite dimensional irreducible representation of G. The author obtains some non-vanishing results for the cohomology space \(H^*(\Gamma,F)\) in the case of \(G=Sp(p,q)\) (p\(\geq q\geq 1)\). It is shown that the first possible non-zero cohomology \(H^*(\Gamma,F)\) appears at the degree \(2q=r_ G\).