# The structure of highest weight representations

*Algebra/Geometry/Topology Seminar*

*by Rahbar Virk*

*Institution:*U. Wisconsin

*Date: Thu 10th December 2009*

*Time: 2:15 PM*

*Location: 213 Richard Berry*

*Abstract*: will give an introduction to the representation theory of highest weight modules of a simple Lie algebra over the complex numbers. Several classical tools in the theory, such as the Harish-Chandra isomorphism, category O, BGG-reciprocity and Jantzen's translation principle, will be highlighted. Time permitting, I will explain how working with derived categories leads naturally to the appearance of the braid group which in turn further elucidates many aspects of the theory. Throughout, I will emphasize the examples of sl_2 and sl_3.

*For More Information:* craigw@ms.unimelb.edu.au