Coherent Sheaves on Quiver Varieties and Categorification
  We construct geometric categorical Lie algebra actions on the derived category of coherent sheaves on Nakajima quiver varieties. These actions categorify Nakajima's construction of Kac-Moody algebra representations on the K-theory of quiver varieties. We define an induced affine braid group action on these derived categories. 
Sabin Cautis, Joel Kamnitzer and Anthony Licata
math.AG math.RT