We re-examine some topics of representation theory in the more general context of conical symplectic resolutions. In part I, we consider a version of the Beilinson-Bernstein localization theorem, the theory of Harish-Chandra bimodules and a generalization of twisting functors.

In part II. we define and study category O for a symplectic resolution, with many strong parallels to the BGG case. We observe that category O is often Koszul, and its Koszul dual is often equivalent to category O for a different symplectic resolution. This leads us to define the notion of a symplectic duality between symplectic resolutions, which includes a Koszul duality between the two categories O .