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

Arkady Berenstein·Reyer Sjamaar
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Abstract

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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Arkady Berenstein, Reyer Sjamaar. 1999-11-25. Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion. https://arxiv.org/abs/math/9810125

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