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 s(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：s(2，C)
§1.6.Finite Dimensional Modules
§1.7.Action of the Center
§1.8.Central Characters and Linked Weights
§1.9.Harish-Chandra Homomorphism
§1.10.Harish-Chandra's Theorem
§1.11.Category O is Artinian
§1.12.Subcategories OX
§1.13.Blocks
§1.14.Formal Characters of Finite Dimensional Modules
§1.15.Formal Characters of Modules in O
§1.16.Formal Characters of Verma Modules
Notes
Chapter 2. Characters of Finite Dimensional Modules
§2.1.Summary of Prerequisites
§2.2.F0rmal Characters Revisited
§2.3.The Functions P and q
§2.4.Formulas of Weyl and Kostant
§2.5.Dimension Formula
§2.6.Maximal Submodule of M(λ)，入∈Λ+
§2.7.Related Topics
Notes
Chapter 3.Category O：Methods
§3.1.Horn and Ext
§3.2.Duality in O
§3.3.Duals of Highest Weight Modules
§3.4.The Reflection Group W[λ]
§3.5.Dominant and Antidominant Weights
§3.6.Tensoring Verma Modules with Finite Dimensional Modules
§3.7.Standard Filtrations
§3.8.Projectives in O
§3.9.Indecomposable Projectives
§3.10.Standard Filtrations of Projectives
