Course Description and Grading BreakdownIf 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 LocationMonday, Wednesday and Friday 11:00 - 11:55 am 387 Linde Course Instructor Contact Information and Office Hours281 Linde Hall Course Schedule and TextbookLectures on Lie Groups by J. Frank Adams, 1969 ISBN: 0-226-00530-5
Course PoliciesLate work - Assignments
Midterm and Final ExamCollaboration Table
* 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. |