Modular generalized Springer correspondence II: classical groups

Pramod N. Achar (1) , Anthony Henderson (2) , Daniel Juteau (3) , Simon Riche (4)

1 LSU Mathematics - Department of Mathematics [Baton Rouge]
2 School of Mathematics and statistics [Sydney]
3 LMNO - Laboratoire de Mathématiques Nicolas Oresme
4 LMBP - Laboratoire de Mathématiques Blaise Pascal

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(2n) with characteristic-2 coefficients.

Domaines: Théorie des représentations [math.RT]; Mathématiques [math]

Pramod N. Achar, Anthony Henderson, Daniel Juteau, Simon Riche. Modular generalized Springer correspondence II: classical groups. Journal of the European Mathematical Society, 2017, 19, pp.1013-1070. ⟨hal-00974454v3⟩