Abstract

The idea of categorification provides better understanding of rich structures associated with quantum groups and provides links between different representation categories. In this talk, we will explain an equivalence between a category of representations of quiver Hecke algebras for the Kronecker quiver and the category of equivariant perverse coherent sheaves on the nilpotent cone of type A. Both of them provides categorification of certain part of the quantum loop algebras of sl_2.