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
DOI:
https://doi.org/10.1090/S1088-4165-09-00364-1
Published electronically:
November 4, 2009
MathSciNet review:
2558787
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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Additional Information
Ting Xue
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email:
txue@math.mit.edu
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.