Geometry and Topology of Coadjoint Orbits of Semisimple Lie Groups

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.