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

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

2009-11-06

arxiv.org/abs/0911.1350v1

Mathematics

Representation Theory

30 pages

Scientific paper

We give a combinatorial description of the Springer correspondence for classical Lie algebras $\Lg$ of type $B,C$ or $D$ and their duals $\Lg^*$ 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 $G$, $\Lg$ and $\Lg^*$ in all characteristics. Moreover, it gives rise to close formulas for computing the correspondences.

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