Perverse sheaves over real hyperplane arrangements. II (Q2105136)

Summary: Let \(\mathcal{H}\) be an arrangement of hyperplanes in \(\mathbb{R}^n\) and \(\mathrm{Perv} (\mathbb{C}^n, \mathcal{H})\) be the category of perverse sheaves on \(\mathbb{C}^n\) smooth with respect to the stratification given by complexified flats of \(\mathcal{H}\). We give a description of \(\mathrm{Perv} (\mathbb{C}^n, \mathcal{H})\) in terms of ``matrix diagrams'', i.e., diagrams formed by vector spaces \(E_{A, B}\) labeled by pairs \((A, B)\) of real faces of \(\mathcal{H}\) (of all dimensions) or, equivalently, by the cells \(i A + B\) of a natural cell decomposition of \(\mathbb{C}^n\). A matrix diagram is formally similar to a datum describing a constructible (nonperverse) sheaf but with the direction of one-half of the arrows reversed. For Part I, see the authors' paper [Ann. Math. (2) 183, No. 2, 619--679 (2016; Zbl 1360.14062)].