Journal of the European Mathematical Society

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Volume 19, Issue 4, 2017, pp. 1013–1070
DOI: 10.4171/JEMS/687

Published online: 2017-03-15

Modular generalized Springer correspondence II: classical groups

Pramod N. Achar[1], Anthony Henderson[2], Daniel Juteau[3] and Simon Riche[4]

(1) Louisiana State University, Baton Rouge, USA
(2) University of Sydney, Australia
(3) Université de Caen Basse-Normandie, France
(4) Université Blaise Pascal, Aubière, France

We construct a modular generalized Springer correspondence for any classical group, by generalizing to the modular setting various results of Lusztig in the case of characteristic-0 coefficients.We determine the cuspidal pairs in all classical types, and compute the correspondence explicitly for SL($n$) with coefficients of arbitrary characteristic and for SO($n$) and Sp(2$n$) with characteristic-2 coefficients.

Keywords: Springer correspondence, nilpotent cone, nilpotent orbits, perverse sheaves, cuspidal pairs, distinguished orbits, modular reduction

Achar Pramod, Henderson Anthony, Juteau Daniel, Riche Simon: Modular generalized Springer correspondence II: classical groups. J. Eur. Math. Soc. 19 (2017), 1013-1070. doi: 10.4171/JEMS/687