全英语课程：李群与李代数表示论引论

主讲： 图卢兹大学 J. Sauloy 教授 

时间地点：7-15周，周一（6-8）节，1区数-104；

          6-15周，周三（6-8）节，1区数-104

 
Introduction to the representation theory of Lie groups and Lie algebras
 Note: all the course will be about real and complex Lie groups and algebras.
 
I Introduction with motivating examples drawn from algebra, geometry,
 analysis, number theory and physics
 II Reminders and complements of linear, multilinear and tensor algebra
 III Matrices and matrix groups (algebraic, geometric, topological and
 differential properties)
 IV Linear representations of "abstract" groups
 V Representations of finite groups
 VI Representations of topological (mainly compact) groups
 VII The representations of SL2(C)
 VIII The representations of SO3(R) and SU2(C)
 IX General theory of Lie groups and algebras
 X Classification of semi-simple Lie algebras and applications 
 
Recommended books for the course
 
1) William Fulton and Joe Harris "Representation Theory" (Springer)
 
2) Jean-Pierre Serre "Lie Algebras and Lie Groups" (Benjamin)
 
3) Jean-Pierre Serre "Algèbres de Lie semi-simples complexes" (Benjamin)
 
4) V.S. Varadarajan "Lie Groups, Lie Algebras and their Representations"

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2014年10月11