Math 735 — Fall 2001 Topics in Algebra

This course will deal with topics in the representation theory of (semisimple) Lie algebras, Kac-Moody algebras, quantum groups and relations between them. The minimum prerequisite is a solid knowledge of linear and basic abstract algebra.

The course is meant to be a continuation of Math 649 (Lie algebras) and the topics course Math 739 given by K. Brown in the spring of 2001. But these are not prerequisites, the first topic will provide a review.

Topics (as time permits):
Construction (and classification) of simple Lie algebras, Quantum groups and Kac-Moody algebras

Representation theory

Relations to knot theory, special functions and combinatorics

Kazhdan-Lusztig type character formulas

Textbooks:
Andersen, Notes on quantum groups
J. Jantzen, Lectures on quantum groups
V. Kac, Infinite dimensional Lie algebras
G. Lusztig, Introduction to quantum groups