# 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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