Math 772 (Spring 2018): Lie Groups and Representation Theory II
Instructor: Mahir Bilen Can
Office: Gibson Hall 318 A
Office Hours: By appointment
Email: mahirbilencan@gmail.com
What is a Lie group?
This is the second semester of my course on Lie groups and their representations.
By definition, 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?
- Compact Lie groups vs reductive algebraic groups.
- Basic structure theory of (compact) Lie groups.
- Basic representation theory of compact Lie groups.
Textbooks:
- 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.
Grading:
There will be three take-home exams to be collected within seven days after their assignments. The (rough) dates of these assignments are
- January 31 (Wednesday),
- April 2 (Monday),
- May 2 (Wednesday).