Intro
Preface
Contents
About the Author
Notations
1 Lie Algebras
1.1 Definitions and Examples
1.2 Universal Enveloping Algebras: PBW Theorem
1.3 Solvable and Nilpotent Lie Algebras
1.4 Semi-Simple Lie Algebras
1.5 Extensions of Lie Algebras and Co-homology
2 Semi-Simple Lie Algebras and Root Systems
2.1 Root Space Decomposition
2.2 Root Systems
2.3 Dynkin Diagram and the Classification of Root Systems
2.4 Conjugacy Theorem, Existence and Uniqueness Theorems
3 Representation Theory of Lie Algebras
3.1 Theorems of Ado and Iwasawa

3.2 Cyclic Modules and Weights
3.3 Characters and Harish-Chandra's Theorem
3.4 Multiplicity Formulas of Weyl, Kostant, and Steinberg
4 Chevalley Groups
4.1 Classical Linear Groups
4.2 Chevalley Basis
4.3 Chevalley Groups
4.4 Twisted Groups
5 Representation Theory of Chevalley Groups
5.1 Language of Representation Theory
5.2 Representations of Sn, and of GL(2.q)
5.3 Steinberg Characters
5.4 Principal and Discrete Series Representations
5.5 Deligne-Lusztig Generalized Characters
Appendix Bibliography
Index