Columbia University W4044 section 001 Representations of finite groups

Basic information

 Call number: 92198 Room/Time: MW 1:10pm--2:25pm, 520 Math Instructor: Mikhail Khovanov Office: 517 Math Office Hours: Walk-in or by appointment E-mail: khovanov@math.columbia.edu TA: Qi You Discussions: Monday 9-10am, Room 622 Office Hours: Tue 6-7pm or by appointment, Room 610 E-mail: yq2121@math.columbia.edu Midterm: Wednesday, Nov 4 Final: Monday, Dec 21, 1:10pm-4pm, MAT 520 Webpage: www.math.columbia.edu/~khovanov/finite

Resources

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.

There is at least a dozen textbooks on representations of finite groups in the library---here's a sample:
J.-P. Serre, Linear representations of finite groups.
B. Sagan, The symmetric group.
B. Simon, Representations of finite and compact groups.
G.James and M.Liebeck, Representations and characters of groups.

Syllabus

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.
Category theory.
The McKay correspondence, Dynkin diagrams, reflection groups.
Representations of the symmetric group.
Representations of quivers.

Homework, quizzes, exams

Homework 1     Homework 2     Homework 3     Homework 4

Homework 5     Homework 6     Homework 7     Homework 8

Homework 9     Homework 10     Homework 11     Homework 12

Practice quiz 1     Quiz 1     Quiz 2     Midterm     Final

Quizzes and exams from 2006 class:

Practice quiz     Practice midterm     Midterm     Final

Representations of groups

C.Teleman, Representation theory
P.Diaconis, Group representations in probability and statistics
W.Miller, Symmetry, Groups and Their Applications
J.Rabinoff, Fourier analysis on finite groups and Schur orthogonality
P.Garrett, Representations of GL(2) and SL(2) over finite fields
D.Joyner, Notes on trace formulas for finite groups
T.Y.Lam, Representations of finite groups: A hundred years, Part I  Part II
T.Deshpande, Representations of finite groups of Lie type
Groups and representation theory notes   Topics in representation theory
D.Panyushev, Lectures on representations of finite groups and invariant theory
Wiki page on reps of finite groups
Materials and links from a course on representation theory at Stanford University
Jeremy Rickard's webpage for a rep theory course
Exercises for Joseph Bernstein's course

Rings and modules

Class notes for Modern Algebra, by Matt Douglass
Notes on Algebra, by Marc Culler Treats rings, modules, modules over PIDs.
A lecture by Daniel Katz on free modules
Condensed review of groups, rings, and modules by Roy Smith
Notes on modules and rings by William Schmitt
Wikipedia's entry on modules
Notes by Ralph Howard

Miscellaneous

Zorn's lemma links: Wiki 1 2
Category theory links: 1 2 3 4 5