MT4144 Representation Theory of Finite Groups

(August - November 26, IISER Pune)

Instructor: Dr. Anupam Singh

Audience: 4th year BS-MS, iPhD, and PhD students at IISER Pune

Schedule: Wednesday 11 AM, Thursday 11 AM, Friday 10 AM, LHC 304

Evaluation: Test I - 20%, mid-sem  - 30%, Test II - 20%, end-sem - 30%

Prerequisite: Basic Algebra courses (Groups, Vector spaces, Modules, etc)

Goal of the course: This course introduces the representation theory of finite groups via character theory. The subject of representation theory is quite deep and needed in advanced mathematics (such as number theory, Lie theory, Harmonic Analysis, etc.) courses as well as Physics and Chemistry.

Proposed Content: Basic definitions and properties of representations, character theory and decomposition of regular representations, Maschke's Theorem, examples of irreducible representations and character tables, group rings, induced representations, and Mackey theory. Burnside's pq Theorem.

Textbooks and reference material :

1. Representation Theory of Finite Groups (course notes): Anupam Singh 

2. Representation Theory of Finite Groups: B. Steinberg

3. Linear Representations of Finite Groups: J. P. Serre

4. Representations and Characters of Groups: James and Liebeck

5. Representations of Finite and Compact Groups: B. Simon

Weekly topics covered :

05/08/26  

06/08/26  

07/08/26