  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)^*.
