We will discuss how to realize categories of highest weight representations of affine W-algebras as categories of perverse sheaves on affine flag manifolds, and the modules for affine Hecke algebras which they categorify. Applications, e.g. to character formulas and the Kac-Roan-Wakimoto conjecture, will be discussed. For principal nilpotent elements, this was worked out jointly with Raskin, and the general case is work in progress with Arakawa.
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Geometric Representation Theory and W-algebras.
