School Seminars and Colloquia

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