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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() with coefficients of arbitrary characteristic and for SO() and Sp(2) with characteristic-2 coefficients.
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Pramod N. Achar, Anthony Henderson, Daniel Juteau, Simon Riche, Modular generalized Springer correspondence II: classical groups. J. Eur. Math. Soc. 19 (2017), no. 4, pp. 1013–1070DOI 10.4171/JEMS/687