# Introduction to Whittaker modules (Part 2 of 3)

*by Alexander Kleshchev*

*Institution:*University of Oregon

*Date: Tue 22nd July 2008*

*Time: 10:00 AM*

*Location: Room 107, Richard Berry Bldg, The University of Melbourne*

*Abstract*: Kleshchev (Parts 1,2,3): We will try to motivate the study of finite

W-algebras as a natural part of Lie theory connected to many other

classical objects, such as Whittaker modules, primitive ideals, canonical

bases, polynomial representations of GL(n). We will explain how the

category of finite dimensional modules over a W-algebra of type A

categorifies polynomial representations of GL(n) and sketch a higher level

Schur-Weyl duality between finite W-algebras and (degenerate) cyclotomic

Hecke algebras. W-algebras are generalizations of the Virasoro algebra and

are useful in conformal field theory.

*For More Information:* Stephen Tillmann s.tillmann@ms.unimelb.edu.au