ALT

Abstract

To any root system we associate a labelled, partially ordered graph and a sheaf theory on the graph with coefficients in an arbitrary field k. An extension property then leads to the definition of a certain universal class of sheaves, the Braden-MacPherson sheaves. We formulate a conjecture about the multiplicity of their stalks. This conjecture implies Lusztig's conjecture on the irreducible characters of the simply connected algebraic group over k associated to the root system. Finally we list the proven instances of the conjecture.