  Let G be a reductive algebraic group, with nilpotent cone N and flag variety
G/B. We construct an exact functor from perverse sheaves on N to locally
constant sheaves on G/B, and we use it to study Ext-groups of simple perverse
sheaves on N in terms of the cohomology of G/B. As an application, we give new
proofs of some known results on stalks of perverse sheaves on N.
