A Parameterization of D equivalences of coherent sheaves of symplectic resolutions of a given symplectic singularity

Abstract

Let G be a reductive groups over an algebraically closed field k. Let P^{(i)} be associated parabolic subgroups, and X^{(i)}:=T^*G/P^i. The bounded derived categories of coherent sheaves on X^{(i)} are equivalent, but there is no canonical equivalence. By refining a construction from a previous paper, we construct a local system of categories over a topological space V^0_C, where these categories are assigned to different points in V^0_C. Natural equivalence functors between these categories are parameterized by homotopy classes of paths between the corresponding points.