Combinatorics of the Springer correspondence for classical Lie algebras and their duals in characteristic 2

Abstract

We give a combinatorial description of the Springer correspondence for classical Lie algebras $\mathfrak{g}$ of type $B,C$ or $D$ and their duals ${\mathfrak{g}}^{\ast }$ in characteristic 2. The combinatorics used here is of the same kind as those appearing in the description of (generalized) Springer correspondence for unipotent case of classical groups $G$ by Lusztig in odd characteristic and by Lusztig and Spaltentstein in characteristic 2. It is very nice that this combinatorics gives a unified description for (generalized) Springer correspondences of classical groups in all cases, namely, in $G$, $\mathfrak{g}$ and ${\mathfrak{g}}^{\ast }$ in all characteristics. Moreover, it gives rise to close formulas for computing the correspondences.

30 pages

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