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

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