Preface
1 Calculus on Manifolds
2 Groups and Lie Groups
3 One-Parameter Subgroups and the Exponential M~
4 The Campbell-Baker-Hausdorff Formula
5 The Adjoint Representation
6 Maximal Tori
7 Representation Theory
8 Roots and Weights
9 Weyl's Formulae
10 Differential Operators on Compact Lie Groups
11 The Riemannian Geometry of a Compact Lie Gro
12 The Trace of the Heat Kernel
Appendix 1: The Tensor Product
Appendix 2: Clifford Algebras and the Spin Groups
Solutions and Hints for Selected Exercises
Bibliography
Index
