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Cohomology of symplectic reductions of generic coadjoint orbits

R. F. Goldin·A. -L. Mare
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Abstract

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 λand a parameter in Lie(T)^*.

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R. F. Goldin, A. -L. Mare. 2002-10-28. Cohomology of symplectic reductions of generic coadjoint orbits. https://arxiv.org/abs/math/0210434

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