Recollement for perverse sheaves on real hyperplane arrangements

Abstract

Consider the category of perverse sheaves on Cn smooth with respect to the stratification arising from a real hyperplane arrangement. We construct an algebra whose module category is equivalent to this category, building on work of Kapranov-Schechtman. We prove that the standard recollement of perverse sheaves is equivalent to a well-known recollement for algebras. As an application of our results, we give a new description of the category of representations of the fundamental group of the complement of such a hyperplane arrangement. We also identify the modules associated to all simple perverse sheaves, that is, the intersection cohomology complexes. Finally, we generalise our results to W-equivariant perverse sheaves for the reflection arrangement of a finite Coxeter group W, extending work of Weissman. As an application, we identify the modules associated to the equivariant simple perverse sheaves. Show more