# Introduction to W algebras

*by Professor Alexander Kleshchev *

*Institution:*University of Oregon

*Date: Fri 18th July 2008*

*Time: 10:30 AM*

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

*Abstract*: 18 July Friday 10.30am to 12noon Room 107

Introduction to W algebras

22 July Tuesday 12noon to 1pm Room 107

Introduction of Whittaker modules

25 July Friday 10.30am 12noon Room 107

Introduction to cyclotomic Hecke algebras

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.

Whittaker modules are natural generalizations of Verma modules.

Cyclotomic Hecke algebras are quotients of affine Hecke algebras.

Alexander Kleshchev revolutionised the modular representation theory

of the symmetric group

when he proved the rule for restricting a simple S n module to

S n 1. This rule later was connected

to the theory of crystals and to Fock representations. He is an

expert in the fast moving theory of W algebras

and we can expect to learn a lot from him during his visit.

We will plan to go to Thresherman's for lunch after his Friday talks.

*For More Information:* Arun Ram A.Ram@ms.unimelb.edu.au