Representation Theory

Course Description and Grading Breakdown

If one attempts to extend the main results (e.g., finite-dimensional representations are direct sums of irreducibles), of the (complex) representation theory of finite groups to infinite groups, one is naturally led to consider {\em compact} groups; i.e., groups which are also compact topological spaces, in a way compatible with the group structure.  We will discuss how the finite group results carry over, and some of the main structural results on compact groups, in particular the Peter-Weyl theorem (a generalization of the theory of Fourier series).

Of particular interest is the case of compact Lie groups (in which the topology is a manifold); we'll consider their structure in greater detail, with specific attention to the classical compact groups (the unitary, orthogonal, and symplectic groups) and their representations.

We'll also discuss the structure and classification of compact Lie groups, and results of Weyl on the irreducible characters and dimensions of connected compact Lie groups.



Course Meeting Time and Location
Monday, Wednesday and Friday
11:00 - 11:55 am
387 Linde

Course Instructor Contact Information and Office Hours
281 Linde Hall


Course Schedule and Textbook
Lectures on Lie Groups by J. Frank Adams, 1969 ISBN: 0-226-00530-5

 DateTopic 
  
  


Course Policies
Late work - 


Assignments
 Date PostedAssignment Due Date 
   
   


Midterm and Final Exam


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.