Modular generalized Springer correspondence II: classical groups

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.

52 pages. Version 2 corrects a minor mistake in the combinatorics of the type D case; no numbered statements are affected. Version 3 has minor additions, mostly in Section 2; final version, to appear in J. Eur. Math. Soc

References in corpus (1)

• Weyl group actions on the Springer sheaf

Cited by in corpus (2)

• Modular generalized Springer correspondence III: exceptional groups
• Modular generalized Springer correspondence: an overview