Etingof conjecture for quantized quiver varieties II: affine quivers

Abstract: We study the representation theory of quantizations of Gieseker moduli spaces. Namely, we prove the localization theorems for these algebras, describe their finite dimensional representations and two-sided ideals as well as their categories O in some special cases. We apply this to prove our conjecture with Bezrukavnikov on the number of finite dimensional irreducible representations of quantized quiver varieties for quivers of affine type.