Perverse sheaves, Koszul IC-modules, and the quiver for the category O

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dc.creatorVybornov, Maxim
dc.date2003-09-15
dc.date2006-06-03
dc.date.accessioned2026-07-07T06:35:43Z
dc.date.available2026-07-07T06:35:43Z
dc.descriptionFor 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.
dc.descriptionNEW: final version to appear in Inventiones Mathematicae. Some exposition revisions. Quiver computed explicitly for A_2 in the appendix. 29 pages
dc.identifierhttps://arxiv.org/abs/math/0309247
dc.identifierhttp://arxiv.org/abs/math/0309247
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99875
dc.subjectAlgebraic Geometry
dc.subjectAlgebraic Topology
dc.subjectRepresentation Theory
dc.titlePerverse sheaves, Koszul IC-modules, and the quiver for the category O
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