[Modules projectifs dans la cohomologie d'intersection des variétiés de Deligne–Lusztig]
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.
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.
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@article{CRMATH_2014__352_6_467_0,
author = {Dudas, Olivier and Malle, Gunter},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.03.011/}
}
TY - JOUR AU - Dudas, Olivier AU - Malle, Gunter TI - Projective modules in the intersection cohomology of Deligne–Lusztig varieties JO - Comptes Rendus. Mathématique PY - 2014 SP - 467 EP - 471 VL - 352 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.03.011/ DO - 10.1016/j.crma.2014.03.011 LA - en ID - CRMATH_2014__352_6_467_0 ER -
%0 Journal Article %A Dudas, Olivier %A Malle, Gunter %T Projective modules in the intersection cohomology of Deligne–Lusztig varieties %J Comptes Rendus. Mathématique %D 2014 %P 467-471 %V 352 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.03.011/ %R 10.1016/j.crma.2014.03.011 %G en %F CRMATH_2014__352_6_467_0
Dudas, Olivier; Malle, Gunter. Projective modules in the intersection cohomology of Deligne–Lusztig varieties. Comptes Rendus. Mathématique, Tome 352 (2014) no. 6, pp. 467-471. doi : 10.1016/j.crma.2014.03.011. http://www.numdam.org/articles/10.1016/j.crma.2014.03.011/
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