Contents
Preface
Chapter 0. Review of Semisimple Lie Algebras
§0.1. Cartan Decomposition
§0.2. Root Systems
§0.3. Weyl Groups
§0.4. Chevalley-Bruhat Ordering of W
§0.5. Universal Enveloping Algebras
§0.6. Integral Weights
§0.7. Representations
§0.8. Finite Dimensional Modules
§0.9. Simple Modules for sl(2, C)
Part I. Highest Weight Modules
Chapter 1. Category O: Basics
§1.1. Axioms and Consequences
§1.2. Highest Weight Modules
§1.3. Verma Modules and Simple Modules
§1.4. Maximal Vectors in Verma Modules
§1.5. Example: si(2,C)
§1.6. Finite Dimensional Modules
§1.7. Action of the Center
§1.8. Central Characters and Linked Weights
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