Columbia University W4044 section 001
Representations of finite groups

Basic information

Call number: 29574
Room/Time: MW 1:10pm--2:25pm, 520 Math
Instructor: Mikhail Khovanov
Office: 517 Math
Office Hours: MW 3-4
E-mail: khovanov@math.columbia.edu
 
Midterm: Wednesday, March 8
Final: Monday, May 8, 1:10pm, 517 Math
Webpage: www.math.columbia.edu/~khovanov/finite
 

Syllabus and text

Textbook: Representations and characters of groups, second edition, by Gordon James and Martin Liebeck (the paperback edition is much cheaper than the hardcover one).

The following books will be placed on reserve in the math library:
B. Sagan, The symmetric group.
J.-P. Serre, Linear representations of finite groups.
B. Simon, Representations of finite and compact groups.


Syllabus:
Groups and their actions on sets.
Actions of groups on vector spaces, representations.
Group algebras, modules, complete reducibility.
Schur's lemma, irreducible modules, characters, orthogonality relations.
Tensor product of representations.
Restriction and induction.
Applications of representation theory.
Representations of algebras and rings.
The McKay correspondence, Dynkin diagrams, reflection groups.
Representations of the symmetric group.

Homework


Homework 1       Homework 2       Homework 3       Homework 4       Homework 5      

Homework 6       Homework 7       Homework 8       Homework 9       Homework 10      

Exams


Practice midterm       Midterm       Final