---

MATH 629

Problem Sets

Exam and Projects

Lie Groups
Math 629
Exam and Projects

Midterm Exam
The midterm exam is an in-class exam and is  scheduled for Monday, March 25.  The exam will cover material from the beginning of our text through Chapter 4.3. It will not be a very hard exam but you should know all the basic definitions and all the major theorems, as well as have a good grasp of the problems I have assigned throughout the semester.

Projects
There are a variety of projects you can choose from. You are expected to read a fair amount of material and prepare a presentation for the class. This material will be posted here by mid-February. For now, the items below are just thoughts to give you an idea, but they are not yet flushed out. The projects must be approved by me.

Project 1. Borel Weil Construction of Representations (Brent)

Project 2. Fundamental groups of certain Lie groups (George)

Project 3. Weyl group actions. (Tony)

Project 4. Some relationships to Symplectic Geometry (T-equivariant cohomology)

Project 5. Relationships among matrix Lie groups (which ones are isomorphic to which, which ones are covering spaces of which, which ones are maximal compact subgroups of others). Also, the implications of these relationships for representations of these Lie groups.

Project 6. Represetations of finite groups, and in particular, Sn. (Sam)

Project 7. Lie group representations in physics.