紧李群目录

Preface1 Compact Lie Groups1.1 Basic Notions1.2 Basic Topology1.3 The Double Cover of SO(n)1.4 Integration2 Representations2.1 Basic Notions2.2 Operations on Representations2.3 Examples of Irreducibility3 Harmonic Analysis3.1 Matrix Coefficients3.2 Infinite-Dimensional Representations3.3 The Peter-Weyl Theorem3.4 Fourier Theory4 Lie Algebras4.1 Basic Definitions4.2 Further Constructions5 Abelian Lie Subgroups and Structure5.1 Abelian Subgroups and Subalgebras5.2 Structure6 Roots and Associated Structures6.1 Root Theory6.2 The Standard s[(2, C) Triple6.3 Lattices6.4 Weyl Group7 Highest Weight Theory7.1 Highest Weights7.2 Weyl Integration Formula7.3 Weyl Character Formula7.4 Borel-Weil TheoremReferencesIndex