  In this paper, we describe a categorical action of any Kac-Moody algebra on a
category of quantized coherent sheaves on Nakajima quiver varieties. By
"quantized coherent sheaves," we mean a category of sheaves of modules over a
deformation quantization of the natural symplectic structure on quiver
varieties. This action is a direct categorification of the geometric
construction of universal enveloping algebras by Nakajima.
