Contents
Preface xv
Introduction xvii
Chapter 1. Geometry of Coadjoint Orbits 1
§1. Basic definitions 1
1.1. Coadjoint representation 1
1.2. Canonical form σΩ 4
§2. Symplectic structure on coadjoint orbits 5
2.1. The first (original) approach 6
2.2. The second (Poisson) approach 7
2.3. The third (symplectic reduction) approach 9
2.4. Integrality condition 11
§3. Coadjoint invariant functions 14
3.1. General properties of invariants 14
3.2. Examples 15
§4. The moment map 16
4.1. The universal property of coadjoint orbits 16
4.2. Some particular cases 19
§5. Polarizations 23
5.1. Elements of symplectic geometry 23
5.2. Invariant polarizations on homogeneous symplectic man-
ifolds 26
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