Preprint

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.

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

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Friday, April 4, 2014