Decomposition numbers for perverse sheaves
Annales de l'Institut Fourier, Volume 59 (2009) no. 3, p. 1177-1229

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 nilpotent 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.

Le but de cet article est de poser les fondations pour les nombres de décomposition des faisceaux pervers, de donner quelques méthodes pour les calculer dans des cas simples et de les déterminer explicitement dans deux situations : pour une singularité simple (kleinienne) de surface et pour l’adhérence de l’orbite nilpotente non-triviale minimale dans une algèbre de Lie simple.

Ce travail a des applications dans la théorie des représentations modulaires, pour les groupes de Weyl en utilisant le cône nilpotent de l’algèbre de Lie semi-simple correspondante, et pour les schémas en groupes réductifs en utilisant la grassmannienne affine du dual de Langlands.

DOI : https://doi.org/10.5802/aif.2461
Classification:  55N33,  20C20
Keywords: Perverse sheaves, intersection cohomology, integral cohomology, t-structures, torsion theories, decomposition matrices, simple singularities, minimal nilpotent orbits
@article{AIF_2009__59_3_1177_0,
     author = {Juteau, Daniel},
     title = {Decomposition numbers  for perverse sheaves},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {3},
     year = {2009},
     pages = {1177-1229},
     doi = {10.5802/aif.2461},
     mrnumber = {2543666},
     zbl = {1187.14022},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2009__59_3_1177_0}
}
Juteau, Daniel. Decomposition numbers  for perverse sheaves. Annales de l'Institut Fourier, Volume 59 (2009) no. 3, pp. 1177-1229. doi : 10.5802/aif.2461. http://www.numdam.org/item/AIF_2009__59_3_1177_0/

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