:量子群和晶体基引论(影印版)

Introduction
Chapter 1． Lie Algebras and Hopf Algebras
1．1． Lie algebras
1．2． Representations of Lie algebras
1．3． The Lie algebra 8[（2， F）
1．4． The special linear Lie algebra [（n， F）
1．5． Hopf algebras
Exercises

Chapter 2． Kac-Moody Algebras
2．1． Kac-Moody algebras
2．2． Classification of generalized Cartan matrices
2．3． Representation theory of Kac-Moody algebras
2．4． The category Oint
Exercises

Chapter 3． Quantum Groups
3．1． Quantum groups
3．2． Representation theory of quantum groups
3．3． Al-forms
3．4． Classical limit
3．5． Complete reducibility of the category oiqt
Exercises

Chapter 4． Crystal Bases
4．1． Kashiwara operators
4．2． Crystal bases and crystal graphs
4．3． Crystal bases for Uq（12）-modules
4．4． Tensor product rule
4．5． Crystals
Exercises

Chapter 5． Existence and Uniqueness of Crystal Bases
5．1． Existence of crystal bases
5．2． Uniqueness of crystal bases
5．3． Kashiwara's grand-loop argument
Exercises

Chapter 6． Global Bases
6．1． Balanced triple
6．2． Global basis for V（A）
6．3． Polarization on Uq （g）
6．4． Triviality of vector bundles over p1
6．5． Existence of global bases
Exercises

Chapter 7． Young Tableaux and Crystals
7．1． The quantum group Uq（ln）
7．2． The category O>
7．3． Tableaux and crystals
7．4． Crystal graphs for Uq（gIn）-modules
Exercises

Chapter 8． Crystal Graphs for Classical Lie Algebras
8．1． Example： Uq（B3）-crystals
8．2． Realization of Uq（An-1）-crystals
8．3． Realization of Uq（Cn）-crystals