Sheaves on moment graphs and a localization of Verma flags

Details Sheaves on moment graphs and a localization of Verma flags Sheaves on moment graphs and a localization of Verma flags

2005-05-06

arxiv.org/abs/math/0505108v2

Adv. Math. 217 (2008), 683-712

Mathematics

Representation Theory

25 pages

Scientific paper

To any moment graph G we assign a subcategory V of the category of sheaves on G together with an exact structure. We show that in the case that the graph is associated to a non-critical block of the equivariant category O over a symmetrizable Kac-Moody algebra, V is equivalent (as an exact category) to the subcategory of modules that admit a Verma flag. The projective modules correspond under this equivalence to the intersection cohomology sheaves on the graph.

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