Abstract: Let i:K' -> K be an inclusion of compact groups. There is an induced map i^*:k^* -> k'^* on the duals of the Lie algebras, and we would like to calculate the image of a coadjoint orbit under this map. Berenstein and Sjamaar (2000) gave a solution to this problem in terms of the cohomology of homogenous spaces K/T and K'/T'. This motivates us to study Schubert calculus of these spaces, and in particular to understand vanishing properties of the map H^*(K/T) -> H^*(K'/T') in the Schubert basis. I will expound this picture, and discuss some techniques which are applicable to the problem.