Preface
Introduction
Chapter 1 Geometry of Coadjoint Orbits
1 Basic definitions
1.1 Coadjoint representation
1.2 Canonical form σΩ
2 Symplectic structure on coadjoint orbits
2.1 The first（original）approach
2.2 The second（Poisson）approach
2.3 The third（symplectic reduction）approach
2.4 Integrality condition
3 Coatijoint invariant functions
3.1 General properties of invariants
3.2 Examples
4 The moment map
4.1 The universal property of eoadjoint orbits
4.2 Some particular cases
5 Polarizations
5.1 Elements of symplectic geometry
5.2 Invariant polarizations on homogeneous symplectic man— ifolds
Chapter 2 Representations and Orbits of the Heisenberg Group
1 Heisenberg Lie algebra and Heisenberg Lie group
1.1 Some realizations
1.2 Universal enveloping algebra u（b）
1.3 The Heisenberg Lie algebra as a contraction
2 Canonical commutation relations
2.1 Creation and annihilation operators
2.2 Two—sided ideals in u（□）
2.3 H.Weyl reformulation of CCR
2.4 The standard realization of CCR
2.5 Other realizations of CCR
2.6 Uniqueness theorem
3 Representation theory for the Heisenberg group
3.1 The unitary dual H
3.2 The generalized characters of H
3.3 The infinitesimal characters of H
3.4 The tensor product of unirreps
4 Coadjoint orbits of the Heisenberg group
4.1 Description of coadjoint orbits
4.2 Symplectic forms on orbits and the Poison structure on □
4.3 Projections of eoadjoint orbits
5 Orbits and representations
5.1 Restriction—induction principle and construction of unirreps
5.2 Other rules of the User’s Guide
6 Polarizations
6.1 Real polarizations
6.2 Complex polarizations
6.3 Discrete polarizations
Chapter 3 The Orbit Method for Nilpotent Lie Groups
1 Generalities on nilpotent Lie groups
2 Comments on the User’s Guide
2.1 The unitary dual
……
Chapter 4 Solvable Lie Groups
Chapter 5 Compact Lie Groups
Chapter 6 Miscellaneous
Appendix Ⅰ Abstract Nonsense
Appendix Ⅱ Smooth Manifolds
Appendix Ⅲ Lie Groups and Homogeneous Manifolds
Appendix Ⅳ Elements of Functional Analysis
Appendix Ⅴ Representation Theory
References
Index
