Projective modules in the intersection cohomology of Deligne–Lusztig varieties

Olivier Dudas; Gunter Malle

doi:10.1016/j.crma.2014.03.011

Group theory

Projective modules in the intersection cohomology of Deligne–Lusztig varieties

Presented by: the Editorial Board

Olivier Dudas ¹; Gunter Malle ²

¹ Université Paris-Diderot, UFR de mathématiques, bâtiment Sophie-Germain, 5, rue Thomas-Mann, 75205 Paris cedex 13, France
² FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany

Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 467-471.

Abstract
Résumé

We formulate a strong positivity conjecture on characters afforded by the Alvis–Curtis dual of the intersection cohomology of Deligne–Lusztig varieties. This conjecture provides a powerful tool to determine decomposition numbers of unipotent ℓ-blocks of finite reductive groups.

Nous formulons une conjecture de positivité sur le dual d'Alvis–Curtis du caractère obtenu à partir de la cohomologie d'intersection d'une variété de Deligne–Lusztig. Cette conjecture se révèle être un outil puissant pour déterminer les nombres de décompositions des ℓ-blocs unipotents des groupes réductifs finis.

Received: 2014-02-13
Accepted: 2014-03-07
Published online: 2014-04-13

DOI: 10.1016/j.crma.2014.03.011

Author's affiliations:

Olivier Dudas ¹; Gunter Malle ²

¹ Université Paris-Diderot, UFR de mathématiques, bâtiment Sophie-Germain, 5, rue Thomas-Mann, 75205 Paris cedex 13, France
² FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany

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     author = {Olivier Dudas and Gunter Malle},
     title = {Projective modules in the intersection cohomology of {Deligne{\textendash}Lusztig} varieties},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {467--471},
     publisher = {Elsevier},
     volume = {352},
     number = {6},
     year = {2014},
     doi = {10.1016/j.crma.2014.03.011},
     language = {en},
}

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Olivier Dudas; Gunter Malle. Projective modules in the intersection cohomology of Deligne–Lusztig varieties. Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 467-471. doi : 10.1016/j.crma.2014.03.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.03.011/

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