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Inventiones mathematicae

, Volume 211, Issue 2, pp 579–589 | Cite as

Modular irreducibility of cuspidal unipotent characters

  • Olivier Dudas
  • Gunter Malle
Article

Abstract

We prove a long-standing conjecture of Geck which predicts that cuspidal unipotent characters remain irreducible after \(\ell \)-reduction. To this end, we construct a progenerator for the category of representations of a finite reductive group coming from generalised Gelfand–Graev representations. This is achieved by showing that cuspidal representations appear in the head of generalised Gelfand–Graev representations attached to cuspidal unipotent classes, as defined and studied in Geck and Malle (J Lond Math Soc 2(53):63–78, 1996).

Mathematics Subject Classification

Primary 20C33 Secondary 20C08 

Notes

Acknowledgements

We thank Meinolf Geck and Jay Taylor for valuable comments on an earlier version.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Université Paris Diderot, UFR de Mathématiques, Bâtiment Sophie GermainParis Cedex 13France
  2. 2.FB MathematikTU KaiserslauternKaiserslauternGermany

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