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

2003/09/15 by Vybornov, Maxim
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0309247

Abstract

For a stratified topological space we introduce the category of IC-modules, which are linear algebra devices with the relations described by the equation d²=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.

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