Geometry and topology of coadjoint orbits of semisimple Lie groups. (English) Zbl 1208.22009

Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 146-166 (2008).
Summary: Orbits of coadjoint representations of classical compact Lie groups have a lot of applications. They appear in representation theory, geometrical quantization, theory of magnetism, quantum optics, etc. As geometric objects the orbits were the subject of extensive study. However, they remain hard for calculation and application. We propose a simple solution for the following problem: an explicit parametrization of the orbit by means of a generalized stereographic projection, which provide a Kählerian structure on the orbit, and basis two-forms for the cohomology group of the orbit.
For the entire collection see [Zbl 1154.17001].


22E46 Semisimple Lie groups and their representations
53D20 Momentum maps; symplectic reduction
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