Sheaves on moment graphs and a localization of Verma flags
By P. Fiebig. 2005
55 citations recorded by the source corpus.
Abstract 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, and hence, by a theorem of Braden and MacPherson, to the equivariant intersection cohomologies of Schubert varieties associated to Kac–Moody groups.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/82a38d927ad5994deef0cf2b9f81213f2cd63b31
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
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Citations in the corpus
- The combinatorics of Coxeter categories (2005, methodology): “We want to explain the representation theoretic content of V. The following will not be used in the sequel. More details can be found in [ Fie2 ].”
- Sheaves on affine Schubert varieties, modular representations and Lusztig's conjecture (2007, unknown): “A large part of the theory of k -sheaves on a moment graph G behaves well only in the case that the pair ( G , k ) satisfies the GKM-property, which means that the labels on two different edges meeting at a common vertex are linearly independent over k (cf. [Fie08a]).”