QUANTUM
   INTEGRABLE
   SYSTEMS and
   GEOMETRY
   2012









 3-7 SEPTEMBER 2012
 OLHÃO, PORTUGAL

The sl(3) web algebra

Marco Mackaay

(download presentation)

In my talk I will start by recalling the definition of Khovanov's arc algebra H(n), which is closely related to his original categorification of the Jones polynomial. The arc algebra also shows up in the algebro-geometric approach to categorification due to Kamnitzer and Cautis and the representation theoretic approach due to Stroppel and Mazorchuk.

I will then explain my joint work with Weiwei Pan and Daniel Tubbenhauer on the sl(3) web algebra K(S), which is the sl(3) analogue of H_n. We defined K(S) in a recent paper and proved some basic properties, which I will explain. I will also comment on the relation of K(S) with the algebro-geometric and the representation theoretic approaches to categorification.