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Parity Sheaves
Given a stratified variety X with strata satisfying a cohomological parity-vanishing condition, we define and show the uniqueness of “parity sheaves”, which are objects in the constructible derivedExpand
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Generic singularities of nilpotent orbit closures
According to a well-known theorem of Brieskorn and Slodowy, the intersection of the nilpotent cone of a simple Lie algebra with a transverse slice to the subregular nilpotent orbit is a simpleExpand
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Parity sheaves and tilting modules
We show that tilting modules and parity sheaves on the affine Grassmannian are related through the geometric Satake correspondence, when the characteristic is bigger than an explicit bound.
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Modular Springer correspondence and decomposition matrices
In 1976, Springer defined a correspondence making a link between the irreducible ordinary (characteristic zero) representations of a Weyl group and the geometry of the associated nilpotent variety.Expand
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Perverse sheaves and modular representation theory
This paper is an introduction to the use of perverse sheaves with positive characteristic coefficients in modular representation theory. In the first part, we survey results relating singularities inExpand
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Decomposition numbers for perverse sheaves
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 twoExpand
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Parabolic degeneration of rational Cherednik algebras
We introduce parabolic degenerations of rational Cherednik algebras of complex reflection groups, and use them to give necessary conditions for finite-dimensionality of an irreducible lowest weightExpand
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Modular Springer correspondence, decomposition matrices and basic sets
The Springer correspondence makes a link between the characters of a Weyl group and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra. In this article, we consider aExpand
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Modular generalized Springer correspondence II: classical groups
We construct a modular generalized Springer correspondence for any classical group, by generalizing to the modular setting various results of Lusztig in the case of characteristic-0 coefficients. WeExpand
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Modular generalized Springer correspondence I: the general linear group
We define a generalized Springer correspondence for the group GL(n) over any field. We also determine the cuspidal pairs, and compute the correspondence explicitly. Finally we define a stratificationExpand
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