Course Description and other details:

Course: MA 220

The plan is to cover the following topics in this course. 

  • Groups and their actions on sets. 
  • Modules over rings and algebras, simple modules, Schur's lemma. 
  • Actions of groups on vector spaces, representations. 
  • Group algebras, modules, complete reducibility, Wedderburn's theorem. 
  • Characters, orthogonality relations. 
  • Tensor product of representations. 
  • Restriction and induction. 
  • Applications of representation theory. 
  • Representations of the symmetric group. 
  • Polynomial representations of GL_n(K) 

Books available in Library/Tata Book House

  1. J.-P. Serre, Linear representations of finite groups. 
  2. B. Sagan, The symmetric group. 
  3. Martin Issacs: Character theory of finite Groups
  4. Amritanshu Prasad: Representation Theory 
  5. G.James and M.Liebeck, Representations and characters of groups.
  6. K.Erdmann, J.A.Green, M. Schoker, Polynomial Representations of GL_n. 

Online textbooks:

P.Webb, Representation Theory Book We need the first 5 sections (pages 1-62).
A.Baker, Representations of finite groups
A.N.Sengupta, Notes on representations of algebras and finite groups
D.M.Jackson, Notes on the representation theory of finite groups

P.Etingof et al. Introduction to representation theory also discusses category theory, Dynkin diagrams, and representations of quivers.


Grading:

20 %: Class tests

30%: Mid Sem (2-4pm on September 19th, 2017 )

50%: Final Exam 


Question Sets: 

Que Set-1

First Class test on September 07th, 2017.