Cohomology of symplectic reductions of generic coadjoint orbits
Symplectic Geometry
2007-05-23 v1 Algebraic Geometry
Combinatorics
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 \lambda and a parameter in Lie(T)^*.
Cite
@article{arxiv.math/0210434,
title = {Cohomology of symplectic reductions of generic coadjoint orbits},
author = {R. F. Goldin and A. -L. Mare},
journal= {arXiv preprint arXiv:math/0210434},
year = {2007}
}
Comments
6 pages. This is a generalization of work done by the first author for SU(n), at math.SG/0201138 published Advances in Mathematics 160 (2001), no. 2, pp. 175-204