2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99875For a stratified topological space we introduce the category of IC-modules, which are linear algebra devices with the relations described by the equation d^2=0. We prove that the category of (mixed) IC-modules is equivalent to the category of (mixed) perverse sheaves for flag varieties. As an application, we describe an algorithm calculating the quiver underlying the BGG category O for arbitrary simple Lie algebra, thus answering a question which goes back to I. M. Gelfand.NEW: final version to appear in Inventiones Mathematicae. Some exposition revisions. Quiver computed explicitly for A_2 in the appendix. 29 pagesAlgebraic GeometryAlgebraic TopologyRepresentation Theorytext