Type: Seminar

Distribution: World

Expiry: 23 Apr 2010

Auth: benw@bari.maths.usyd.edu.au

The CRT working group meets again this Friday at 3.30pm in Carslaw 159. This week, we are fortunate to have Andrew Mathas speaking. A preliminary abstract appears below. I hope to see you there! The Brundan-Kleschev categorification theorem in type A Speaker: Andrew Mathas, Carslaw 159, 3.30pm. In the representation theory of Hecke algebras, one of the landmark theorems of the 1990s was Ariki’s proof of the LLT conjecture. In today’s language, Ariki’s theorem says that the (projective) Grothendieck groups of the cyclotomic Hecke algebras give a categorification of the simple highest weight modules L(\Lambda) of the affine special linear group. Moreover, under this categorification, the canonical basis of L(\Lambda) corresponds to the distinguished basis of the Grothendieck groups corresponding to the projective indecomposable modules. In this talk, I will describe Brundan and Kleshchev generalisation of Ariki’s theorem which introduces a grading on the cyclotomic Hecke algebras and lifts this categorification theorem to modules of the quantum affine special group.