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

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

1998-10-20

arxiv.org/abs/math/9810125v2

J. Amer. Math. Soc. 13 (2000), 433-466

Mathematics

Symplectic Geometry

34 pages, 4 figures, revised and reorganized

Scientific paper

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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