Proceedings of the International Conference on Geometry, Integrability and Quantization

Geometry and Topology of Coadjoint Orbits of Semisimple Lie Groups

Julia Bernatska and Petro Holod

Abstract

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.

Article information

Source
Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, ed. (Sofia: Softex, 2008), 146-166

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436793143

Digital Object Identifier
doi:10.7546/giq-9-2008-146-166

Mathematical Reviews number (MathSciNet)
MR2436268

Zentralblatt MATH identifier
1208.22009

Citation

Bernatska, Julia; Holod, Petro. Geometry and Topology of Coadjoint Orbits of Semisimple Lie Groups. Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization, 146--166, Softex, Sofia, Bulgaria, 2008. doi:10.7546/giq-9-2008-146-166. https://projecteuclid.org/euclid.pgiq/1436793143


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