Mathematische Annalen

, Volume 369, Issue 1–2, pp 247–300 | Cite as

Modular generalized Springer correspondence III: exceptional groups

  • Pramod N. Achar
  • Anthony Henderson
  • Daniel Juteau
  • Simon Riche
Article
  • 119 Downloads

Abstract

We complete the construction of the modular generalized Springer correspondence for an arbitrary connected reductive group, with a uniform proof of the disjointness of induction series that avoids the case-by-case arguments for classical groups used in previous papers in the series. We show that the induction series containing the trivial local system on the regular nilpotent orbit is determined by the Sylow subgroups of the Weyl group. Under some assumptions, we give an algorithm for determining the induction series associated to the minimal cuspidal datum with a given central character. We also provide tables and other information on the modular generalized Springer correspondence for quasi-simple groups of exceptional type, including a complete classification of cuspidal pairs in the case of good characteristic, and a full determination of the correspondence in type \(G_2\).

Mathematics Subject Classification

Primary 17B08 20G05 

Notes

Acknowledgements

We are grateful to Jean Michel for implementing many functions on unipotent classes, including the generalized Springer correspondence (with characteristic zero coefficients), in the development version of the GAP3 Chevie package [26]. We would also like to thank the anonymous referee for a careful reading and detailed comments on the paper.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsLouisiana State UniversityBaton RougeUSA
  2. 2.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia
  3. 3.IMJ-PRG, CNRS, UMR 7586Université Paris Diderot - Paris 7PARIS Cedex 13France
  4. 4.Laboratoire de Mathématiques, CNRS, UMR 6620Université Blaise Pascal - Clermont-Ferrand IIAubière CedexFrance

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