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1 The exponential map 1.1
Vector fields and one-parameter groups of linear transformations 1.2 Ad, ad, and dexp 1.3 The Campbell-Baker-Hausdorff Series 2 Lie theory 2.1 Linear groups: definitions and examples 2.2 The Lie algebra of a linear group 2.3 Coordinates on a linear group 2.4 Connectedness 2.6 Homomorphisms and coverings of linear
groups 2.7 Closed subgroups 3 The classical groups 3.1 The classical groups: definitions,
connectedness 3.2 Cartan subgroups 3.3 Roots, weights, reflections 3.4 Fundamental groups of the classical groups |
4 Manifolds,
homogeneous spaces, Lie groups 4.1 Manifolds 4.2 Homogeneous spaces 4.3 General Lie groups 5 Integration 5.1 Integration on manifolds 5.2 Integration on linear groups and their
homogeneous spaces 5.3 Weyl's Integration Formula for U(n) 6 Representations 6.1 Representations: definitions 6.2 Schur's Lemma and its consequences;
Peter-Weyl Theorem 6.3 Characters 6.4 Weyl's Character Formula for U(n) 6.5 Representations of Lie algebras 6.6 The Borel-Weil Theorem for GL(n, C) 6.7
Representations of the classical groups Appendix: The Inverse Function Theorem References Index |
A Mathematica
implementation of Example 1.1.4
by Tony Thrall