  Let W be a smooth complex quasiprojective variety with the action of a
connected reductive group G. Adapting the stratification approach of Teleman to
a microlocal context, we prove a vanishing theorem for the functor of
G-invariant sections---i.e., of quantum Hamiltonian reduction---for
G-equivariant twisted D-modules on W. As a consequence, when W is affine we
establish an effective combinatorial criterion for exactness of the global
sections functors of microlocalization theory. When combined with our earlier
derived equivalence results, this gives precise criteria for "microlocalization
of representation categories."
