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"

教学管理办公室

2014年10月11