Nilpotent orbits in the dual of classical Lie algebras in characteristic 2 and the Springer correspondence

Xue, Ting

doi:10.1090/S1088-4165-09-00364-1

Nilpotent orbits in the dual of classical Lie algebras in characteristic $2$ and the Springer correspondence
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by Ting Xue

Represent. Theory 13 (2009), 609-635

DOI: https://doi.org/10.1090/S1088-4165-09-00364-1

Published electronically: November 4, 2009

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Abstract:

Let $G$ be a simply connected algebraic group of type $B$, $C$ or $D$ over an algebraically closed field of characteristic $2$. We construct a Springer correspondence for the dual vector space of the Lie algebra of $G$. In particular, we classify the nilpotent orbits in the duals of symplectic and orthogonal Lie algebras over algebraically closed or finite fields of characteristic $2$.

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