Cohomology of Flag Varieties and the Brylinski-Kostant Filtration

Details Cohomology of Flag Varieties and the Brylinski-Kostant Filtration Cohomology of Flag Varieties and the Brylinski-Kostant Filtration

2008-03-24

arxiv.org/abs/0803.3424v2

Mathematics

Algebraic Geometry

To appear in J. Algebra. A number of typos fixed; strengthened version of Theorem 4.15 due to anonymous referee

Scientific paper

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.

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