  Let G be a semisimple complex algebraic group with Borel subgroup B and let P
be a parabolic subgroup of G. Let T*(G/P) denote the cotangent bundle of G/P.
Ranee Brylinski discovered a connection between cohomology of G-equivariant
line bundles on T*(G/B) and the so-called Brylinski-Kostant filtration, which
describes the action of principal sl_2 triples on G-representations. In this
paper we generalize these results to a larger class of sl_2 triples. Along the
way we also obtain generalizations of results due to Broer on cohomology of
G-equivariant bundles on T*(G/P) for various parabolics P.

Algebraic Geometry;Representation Theory