Hostname: page-component-5cf477f64f-rdph2 Total loading time: 0 Render date: 2025-04-08T07:26:57.875Z Has data issue: false hasContentIssue false
  • English
  • Français

On Okuyama’s Theorems about Alvis-Curtis Duality

Published online by Cambridge University Press:  11 January 2016

Marc Cabanes
Marc Cabanes*
Affiliation:
Université Paris VII-Denis Diderot, 175, rue du Chevaleret F-75013 Paris, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We report on theorems by T. Okuyama about complexes generalizing the Coxeter complex and the action of parabolic subgroups on them, both for finite BN-pairs and finite dimensional Hecke algebras. Several simplifications, using mainly the surjections of [CaRi], allow a more compact treatment than the one in [O].

Keywords

20C0820C2020C3320J05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 195 , 2009 , pp. 1 - 19
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

References

[B] Benson, D., Representations and Cohomology II: Cohomology of Groups and Modules, Cambridge Univ. Press, Cambridge, 1991.Google Scholar
[CaEn] Cabanes, M. and Enguehard, M., Representation Theory of Finite Reductive Groups, Cambridge Univ. Press, Cambridge, 2004.Google Scholar
[CaRi] Cabanes, M. and Rickard, J., Alvis-Curtis duality as an equivalence of derived categories, Modular Representation Theory of Finite Groups (Collins, M. J., Parshall, B. J., Scott, L. L., eds.), de Gruyter, 2001, pp. 157–174.Google Scholar
[CuRe] Curtis, C. W. and Reiner, I., Methods of Representation Theory with Applications to Finite Groups and Orders, Wiley, 1987.Google Scholar
[DM] Digne, F. and Michel, J., Representations of finite groups of Lie type, Cambridge, 1991.Google Scholar
[GP] Geck, M. and Pfeiffer, G., Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras, Oxford, 2000.Google Scholar
[HL] Howlett, B. and Lehrer, G., On Harish-Chandra induction for modules of Levi subgroups, J. Algebra, 165 (1994), 172–183.Google Scholar
[LS] Linckelmann, M. and Schroll, S., A two-sided q-analogue of the Coxeter complex, J. Algebra, 289 (2005), no. 1, 128–134.Google Scholar
[O] Okuyama, T., On conjectures on complexes of some module categories related to Coxeter complexes, preprint, August 2006, 25 p.Google Scholar
[PS] Parshall, B. and Scott, L., Quantum Weyl reciprocity for cohomology, Proc. London Math. Soc. (3), 90 (2005), 655–688.Google Scholar
[Ri1] Rickard, J., Splendid equivalences: derived categories and permutation modules, Proc. London Math. Soc. (3), 72 (1996), 331–358.Google Scholar
[Ri2] Rickard, J., Triangulated categories in the modular representation theory of finite groups, S. K¨onig and A. Zimmermann, Derived Equivalences for Group Rings, LNM 1685, Springer, 1998, pp. 177–198.Google Scholar
[Ro] Rouquier, R., Block theory via stable and Rickard equivalences, Modular Representation Theory of Finite Groups (Collins, M. J., Parshall, B. J., Scott, L. L., eds.), Walter de Gruyter, 2001, pp. 101–146.Google Scholar