Decomposition numbers for perverse sheaves

By D. Juteau. 2008

50 citations recorded by the source corpus.

The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface singularity, and for the closure of the minimal non-trivial orbit in a simple Lie algebra. This work has applications to modular representation theory, for Weyl groups using the nilpotent cone of the corresponding semisimple Lie algebra, and for reductive algebraic group schemes using the affine Grassmannian of the Langlands dual group.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/77656351af5599bdf2ee27d8160b983fffb9ab20

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In Geometry and Topology

1. Geordie Williamson
2. P. Fiebig
3. Ben Elias
4. Simon Riche
5. T. Arakawa

In Mathematical Physics

1. Geordie Williamson
2. P. Fiebig
3. Ben Elias
4. T. Arakawa
5. Simon Riche

Citations in the corpus

• Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties (2010, background): “onal representations of G. Using the results of this paper we can rephrase the above as follows. Given λ ∈Λ let IC(Xλ,Z) denote the intersection cohomology complex of Xλ with integral coefficients (cf. [Jut09]). Theorem 9.2. Suppose that the stalks and costalks of the intersection cohomology complex I”