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


Authors: Arkady Berenstein and Reyer Sjamaar
Journal: J. Amer. Math. Soc. 13 (2000), 433-466
MSC (2000): Primary 53D20; Secondary 14L24
DOI: https://doi.org/10.1090/S0894-0347-00-00327-1
Published electronically: January 31, 2000
MathSciNet review: 1750957
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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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Additional Information

Arkady Berenstein
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
Address at time of publication: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138-2901
Email: arkadiy@math.harvard.edu

Reyer Sjamaar
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
Email: sjamaar@math.cornell.edu

DOI: https://doi.org/10.1090/S0894-0347-00-00327-1
Received by editor(s): April 30, 1999
Received by editor(s) in revised form: November 21, 1999
Published electronically: January 31, 2000
Additional Notes: The second author was partially supported by an Alfred P. Sloan Research Fellowship and by NSF Grant DMS-9703947
Article copyright: © Copyright 2000 American Mathematical Society

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