Representation Theory of Finite Groups
MTH 411 (August - November 2009)
Reference Material :
TIFR Lecture Notes on Semisimple Rings (thanks to Shripad for LATEXing it)
100 exercises : Raghuram
Representations of GL_2(F_q) : Amritanshu Prasad
Linear Representations of Finite Groups : J. P. Serre
Representations and Characters of Groups : James and Liebeck
Representations of Finite and Compact Groups : B. Simon
Instructor : Anupam Singh
Schedule : August - November 2009, three hours a week
Tuesday 11-12 and 3-4(tutorial)
Wednesday 3-4
Prerequisite : MTH 311 and a good knowledge of Linear Algebra and Basic groups theory
Topics of the course : Basic Representation Theory, Character Theory, Representations of GL_2(F_q).
Notes by K. N. Raghavan who is also giving a course on Representation Theory at IMSc
04/08/09 Definition of Representation
05/08/09 Examples
07/08/09 Examples
Notes for the first 2 weeks of lectures
11/08/09 Teaching suspended due to Swine-Flu-Scare
12/08/09 Teaching suspended due to Swine-Flu-Scare
14/08/09 Teaching suspended due to Swine-Flu-Scare
18/08/09 Teaching suspended due to Swine-Flu-Scare
19/08/09 Teaching suspended due to Swine-Flu-Scare
21/08/09 Teaching suspended due to Swine-Flu-Scare
Maschke's Theorem + Schur's Lemma (also includes revised version of earlier lectures)
25/08/09 No lecture Swine Flu break
26/08/09 No lecture Swine Flue break
28/08/09 No lecture Swine Flu break
Now onwards I will have 2 lectures on Tuesday (one of them tutorial) and one on Wednesday
01/09/09 Projections and Maschke's Theorem
02/09/09 k[G]-modules
04/09/09 (extra lecture) revision of basic group theory e.g. semidirect product, groups of order p^2, p^3 and pq.
08/09/09 Groups of order p^3
09/09/09 Schur's Lemma
15/09/09 Representation Theory of Abelian groups over C
16/09/09 Direct Sum of two Representations and Restrection
22/09/09 Adjoint Representation
23/09/09 Tensor Product of two Representation
29/09/09 I am away!
30/09/09 I am away!
06/10/09 Linear Group GL_n(F_q)
07/10/09 PSL_n(F_q)
13/10/09 mid sem exam
14/10/09 mid sem exam
20/10/09 Seminar (Application of Group Theory in Solving Puzzles) by Dr. Amit Kulshrestha
21/10/09 Seminar
Lecture notes (group theory)
27/10/09 No lecture due to Physics in-house (extra lecture on 2/11)
28/10/09 Character of a Representation
2/11/09 Sum and product of characters
3/11/09 Matrix Elements
4/11/09 Orthogonality of Characters
10/11/09 Regular Representation and it's character
11/11/09 Main Theorem : no. of irreducible characters = no. of conjugacy classes
17/11/09 Character Table
18/11/09 Examples
Notes Representation Theory : includes character theory
24/11/09 Burnside pq Theorem
25/11/09 Representation Theory of (locally) Compact Groups : an overview
01/12/09 Examples of character table
02/12/09 Examples of character table
End Semester Exam