MATH 506 - Group Representation Theory (Spring 2026)

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This is a graduate course in representation theory. The most important prerequisite (by far) is a first course in graduate algebra (Math 500).

A representation is a (linear) action by a group on a vector space. From this straightforward definition, we get a large variety of phenomena which relate to almost every area of mathematics.

The course plan (subject to change) is as follows. We will start with an overview of the representation theory of finite groups, moving into symmetric groups. We will then consider representations of Lie groups and Lie algebras (prior knowledge of Lie theory is not assumed). Finally, we will cover some number of miscellanous topics.

General Information

LectureMWF 10:00am-10:50am
Noyes Laboratory 164
InstructorAndrew Hardt
Office: Harker Hall 204C
Email: ahardt@illinois.edu
Office Hours: MF 11:00am-11:50am, W 2:00pm-2:50pm
More Details Syllabus | Gradescope | If you can't access the Gradescope course, email me

Homework

Homework assignments will be roughly biweekly, generally due at 9am via Gradescope. Using LaTeX for your homework is strongly encouraged.

Lecture Notes

Textbooks and Other Resources

Course Resources

These are the sources we're following most closely in lecture.

Other Representation Theory Material

Other books and notes you might find useful.

Helpful Links

Bonus Links

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