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Representation Theory

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

Author: Ting Xue
Journal: Represent. Theory 13 (2009), 609-635
MSC (2010): Primary 20G15
Published electronically: November 4, 2009
MathSciNet review: 2558787
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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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Ting Xue
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Received by editor(s): February 21, 2009
Received by editor(s) in revised form: September 1, 2009
Published electronically: November 4, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.