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.
Accepté le :
Publié le :
Olivier Dudas 1 ; Gunter Malle 2
@article{CRMATH_2014__352_6_467_0, 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}, }
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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