Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion

@article{Berenstein1998CoadjointOM,
  title={Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion},
  author={Arkady Berenstein and Reyer Sjamaar},
  journal={Journal of the American Mathematical Society},
  year={1998},
  volume={13},
  pages={433-466}
}
Consider a compact Lie group and a closed subgroup. Generalizing a result of Klyachko, we give a necessary and sufficient criterion for a coadjoint orbit of the subgroup to be contained in the projection of a given coadjoint orbit of the ambient group. The criterion is couched in terms of the ``relative'' Schubert calculus of the flag varieties of the two groups. 
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