Math 771 (Fall 2017): Lie Groups and Representation Theory
Instructor: Mahir Bilen Can
Office: Gibson Hall 318 A
Office Hours: By appointment
What is a Lie group?
A Lie group is a differentiable manifold with a group structure where the multiplication and inverse
operations are differentiable maps of manifolds. A representation of a Lie group M is just another way of seeing M as
a group of linear transformations.
What is this course about?
- Definitions, examples, and basic properties of Lie groups and Lie algebras;
- Function theory on (compact) Lie groups;
- Structure of Lie groups;
- Basic representation theory of compact Lie groups.
- Main textbook: Representations of compact Lie groups by Theodor Brocker and Tammo tom Dieck.
- Supplementary: Differential geometry, Lie groups, and symmetric spaces by Sigurdur Helgason.
- Supplementary: The structure of compact groups by Karl H. Hofmann and Sidney A. Morris.
There will be four take-home exams to be collected within seven days after their assignments. The (rough) dates of these assignments are
- September 29 (Friday),
- October 30 (Monday),
- November 20 (Monday),
- December 8 (Friday).