M 392C (57680) Representation Theory

Time: TTH 8:00 – 9:30 am

Room: RLM 12.166

Instructor: Travis Schedler

Course Description:

This course is an introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is, roughly, the study of symmetries acting on vector spaces, a vast generalization of rotational and reflective symmetries.  The course will begin with the classification of (finite-dimensional) irreducible representations of finite groups and associative algebras via character theory, and standard results such as the Jordan-Hoelder and Krull-Schmidt theorems. Then we will discuss the classification and representation theory of finite-dimensional semisimple Lie algebras, and to some extent Lie groups, via root systems and highest weight theory.  Additional topics will be decided with the input of the students. Possible topics include affine algebraic groups, geometric representation theory such as the Borel-Weil theorem or Beilinson-Bernstein theorems, deformations of algebras such as Cherednik algebras, quiver representations, or infinite-dimensional Lie algebras.