### Lusztig's conjecture as a moment graph problem

Fiebig, P *(Freiburg)*

Tuesday 23 June 2009, 11:30-12:30

Seminar Room 1, Newton Institute

#### 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.

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