846 - Representations of Lie algebras

This is a continuation of Math 747 from Fall 2009.
We will continue to investigate semisimple Lie algebras
over the complex numbers, this time with a focus on their representations.
Topics will include: The universal enveloping algebra,
the PBW theorem, Verma modules, classification
of finite-dimensional irreducible modules,
the ring of polynomial invariants, the Casimir element,
character and dimension formulae, fundamental modules.

The lectures will be self contained with complete proofs.
This course should be valuable to anyone interested in
Lie theory, quantum groups, algebraic combinatorics,
number theory, and special functions.