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/Notes:

  1. P.Webb, Representation Theory Book We need the first 5 sections (pages 1-62).
  2. A.BakerRepresentations of finite groups
  3. A.N.SenguptaNotes on representations of algebras and finite groups
  4. D.M.Jackson, Notes on the representation theory of finite group
  5. P.Etingof et al. Introduction to representation theory also discusses category theory, Dynkin diagrams, and representations of quivers.
  6. Hua-Chieh Li, A note on complex representations representations of GL_2(F_q) 

 


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.  

Que Set-2 

Second class test on November 14th, 2017

Que Set-3

Third class test on November 23rd, 2017


Final Exam on December 09th, 2017. 


More exercises on basic representation theory are available here Thanks to Prof. A Raghuram for this compilation.