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).