Math 506 Representation Theory Fall 2021 or Spring 2022, depending on Chair's discretion.

 

Course Title: Representation theory

 

Necessary background: A firm background in linear algebra and abstract algebra.

Suitable for: Students interested in representation theory, mathematical physics, combinatorics, number theory and probably other topics.

Course content:

We'll cover the basic theory of finite or compact group representations, character theory, and representations of the general linear group. We will also make a detour into representations of simple or infinite-dimensional Lie algebras.

 

Textbook: Etingof et al's book notes, Fulton and Harris Representation Theory: A first course.

Course format:

The course will consist of three parts:

  1. In the first part we will cover the basic theorems and definitions from finite group theory, including the standard examples: The symmetric group, the general linear group. Students will be expected to complete simple exercises weekly. Homework will not be graded, but the solutions will be discussed/presented in class where suitable.
  2. In the second part, we will discuss a few more advanced topics (Lie algebras, quivers, infinite dimensional algebras) as time permits.
  3. The last part of the course will consist of student presentations: During the second part of the course there will be many references specialized topics for further study. Each student should pick one of these topics for further study, then present an exposition (a 40 minute talk followed by a discussion).