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

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Let G be a reductive groups over an algebraically closed field k. Let P⁽ⁱ⁾ be associated parabolic subgroups, and X⁽ⁱ⁾:=T*G/Pⁱ. 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 V⁰C, where these categories are assigned to different points in V⁰C. Natural equivalence functors between these categories are parameterized by homotopy classes of paths between the corresponding points.