## Modular generalized Springer correspondence II: classical groups

### Pramod N. Achar, Anthony Henderson, Daniel Juteau and Simon Riche

#### Abstract

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 $$\mathrm{SL}(n)$$ with coefficients of arbitrary characteristic and for $$\mathrm{SO}(n)$$ and $$\mathrm{Sp}(2n)$$ with characteristic-$$2$$ coefficients.

: Primary 17B08, 20G05; Secondary 14M15.

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 Friday, April 4, 2014