Cohomology of symplectic reductions of generic coadjoint orbits

Details Cohomology of symplectic reductions of generic coadjoint orbits Cohomology of symplectic reductions of generic coadjoint orbits

2002-10-28

arxiv.org/abs/math/0210434v1

Proc. Amer. Math. Soc. 132 (2004), no. 10, 3069--3074

Mathematics

Symplectic Geometry

6 pages. This is a generalization of work done by the first author for SU(n), at math.SG/0201138 published Advances in Mathema

Scientific paper

Let mathcal{O}_lambda be a generic coadjoint orbit of a compact semi-simple Lie group K. Weight varieties are the symplectic reductions of mathcal{O}_lambda by the maximal torus T in K. We use a theorem of Tolman and Weitsman to compute the cohomology ring of these varieties. Our formula relies on a Schubert basis of the equivariant cohomology of \mathcal{O}_lambda and it makes explicit the dependence on \lambda and a parameter in Lie(T)^*.

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