[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.
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/
[1] Representations of Finite Groups of Lie Type, Lond. Math. Soc. Stud. Texts, vol. 21, Cambridge University Press, 1991
[2] Cohomologie des variétés de Deligne–Lusztig, Adv. Math., Volume 209 (2007), pp. 749-822
[3] A note on decomposition numbers for groups of Lie type of small rank, J. Algebra, Volume 388 (2013), pp. 364-373
[4] O. Dudas, G. Malle, Decomposition matrices for low rank unitary groups, 2013, submitted for publication.
[5] Basic sets of Brauer characters of finite groups of Lie type II, J. Lond. Math. Soc., Volume 47 (1993), pp. 255-268
[6] Basic sets of Brauer characters of finite groups of Lie type, J. Reine Angew. Math., Volume 418 (1991), pp. 173-188
[7] Modular representations of finite groups of Lie type in non-defining characteristic, Luminy, 1994 (Prog. Math.), Volume vol. 141, Birkhäuser Boston, Boston, MA (1997), pp. 195-249
[8] F. Himstedt, F. Noeske, Decomposition numbers of
[9] The Brauer trees of the exceptional Chevalley groups of types
[10] Unipotente Charaktere und Zerlegungszahlen der endlichen Chevalleygruppen vom Typ
[11] Characters of Reductive Groups over a Finite Field, Ann. Math. Stud., vol. 107, Princeton University Press, Princeton, NJ, 1984
[12] The GAP-part of the Chevie system http://www.math.jussieu.fr/~jmichel/chevie/chevie.html (GAP 3-package available for download from)
- Bounding Harish-Chandra series, Transactions of the American Mathematical Society, Volume 371 (2019) no. 9, pp. 6511-6530 | DOI:10.1090/tran/7600 | Zbl:1515.20069
- Decomposition matrices for exceptional groups at
, Journal of Pure and Applied Algebra, Volume 220 (2016) no. 3, pp. 1096-1121 | DOI:10.1016/j.jpaa.2015.08.009 | Zbl:1383.20013 - Decomposition matrices for low-rank unitary groups, Proceedings of the London Mathematical Society. Third Series, Volume 110 (2015) no. 6, pp. 1517-1557 | DOI:10.1112/plms/pdv008 | Zbl:1364.20005
Cité par 3 documents. Sources : zbMATH
Commentaires - Politique