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Nilpotent orbits in classical Lie algebras over finite fields of characteristic 2 and the Springer correspondence


Author: Ting Xue
Journal: Represent. Theory 13 (2009), 371-390
MSC (2000): Primary 14L35; Secondary 17B10
DOI: https://doi.org/10.1090/S1088-4165-09-00357-4
Published electronically: September 3, 2009
MathSciNet review: 2540701
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Abstract: Let $ G$ be an adjoint algebraic group of type $ B$, $ C$, or $ D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the Lie algebra of $ G$. In particular, for orthogonal Lie algebras in characteristic 2, the structure of component groups of nilpotent centralizers is determined and the number of nilpotent orbits over finite fields is obtained.


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Additional Information

Ting Xue
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: txue@math.mit.edu

DOI: https://doi.org/10.1090/S1088-4165-09-00357-4
Received by editor(s): December 31, 2008
Received by editor(s) in revised form: June 27, 2009
Published electronically: September 3, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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