Categorification in Representation Theory: Mathas -- Brundan-Kleschev Theorem

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.