Representation Theory

Time/Location: 2-4, THU/C701

Syllabus: 

  Part I,  Finite Groups (see [1], [2], [3])

    1.1 Linear representations

    1.2 Character theory

    1.3 The group algebra and representation ring

    1.4 Induced representations and their characters

    1.5 Mackey's subgroup theorem

    1.6 Artin's and Brauer's theorems 

  Part II,  Compact Groups (see [2], [3], [4])

    2.1 Topological groups

    2.2 Linear representations of compact groups

    2.3 Peter-Weyl's theorem

    2.4 Representations of SU(2) and SO(3)

    2.5* Locally comact abelian groups

  Part III，SL(2, R) (see [5], [6], [7])

 (the simplest，nonabelian，noncompact, semisimple lie group )

    3.1 Unitary representations of locally compact groups

    3.2 Principal series representations

    3.3 Complementary and discrete series representations

    3.4 Characters of irreducible representations

    3.5* The Plancherel's theorem for SL(2, R)

    3.6* The Spectrum of L^2(SL(2, Z)\SL(2, R))

References：

1. Serre, Linear Representations of Finite Groups.

2. 冯克勤等，群与代数表示引论.

3. 曹锡华, 叶家琛, 群表示论.

4. 黎景辉, 冯绪宁, 拓扑群引论.

5. Kowalski, An Introduction to the Representation Theory of Groups.

6. Knapp, Representation Theory of Semisimple Groups.

7. Lang, SL(2, R).

8. Mitsuo Sugiura, Unitary Representations and Harmonic Analysis.