Representation Theory

Course Description and Grading Breakdown

The course will focus on representation theory of finite groups. We will talk, roughly, about some of the following things:

a) Representations over an algebraically closed field of characteristic zero. Here, topics include basic theory, characters, induction, Brauer's induction theorem, representations of SL_2(F_q) and S_n.

b) Representations over a field of characteristic zero - up to understanding that if we add enough roots of unity, all representations become realizable, and some more elaboration in the case of the real field.

c) Representations over a field of positive characteristic - up to understanding how many irreducible representations are there.

The grading will be according to homework, which I will publish once in a week or two, and is due 7 days after publication. Each homework will be graded from 0 to 100, and the final numerical grade will be an average of all those. The final letter grade will be roughly according to the following conversion scale:

A+ > 93 > A > 87 > A- > 83 > B+ > 78 > B > 74 > B- > 70 > C+ > 62 > C > 55

The sources for the course will be mainly:

1) "Linear representations of finite groups" by Serre.
2) lecture notes by Etingof.
3) lecture notes by Joseph Bernstein (taken by Adam Gal).
4) Possibly my lecture notes that I will upload.


Course Meeting Time and Location
Lectures
Tuesday and Thursday
1:00 - 2:25 pm
104 Math Building (Building 15)


Course Instructor Contact Information and Office Hours
223 Math Building (Building 15)

Office hours: To be added.


Course Schedule

 DateTopic 
  
  


Course Policies

Late work - The student must ask for permission to hand in the work later than the deadline.


Assignments

 Date PostedAssignment Due Date 
   
   


Collaboration Table

 HomeworkExams
You may consult:  
Course textbook (including answers in the back)YESYES
Other booksYESNO
Solution manualsNONO
InternetYESNO
Your notes (taken in class)YESYES
Class notes of othersYESNO
Your hand copies of class notes of othersYESYES
Photocopies of class notes of othersYESNO
Electronic copies of class notes of othersYESNO
Course handoutsYESYES
Your returned homework / examsYESYES
Solutions to homework / exams (posted on webpage)YESYES
Homework / exams of previous yearsNONO
Solutions to homework / exams of previous yearsNONO
Emails from TAsYESNO
You may:

Discuss problems with othersYESNO
Look at communal materials while writing up solutionsYESNO
Look at individual written work of othersNONO
Post about problems onlineNONO
For computational aids, you may use:

CalculatorsYES*NO
ComputersYES*NO

* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work.  For example, "by Mathematica" is not an acceptable justification for deriving one equation from another.  Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.