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Nilpotent orbits in classical Lie algebras over $textbf{F}_{2^n}$ and the Springer correspondence

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 Added by Ting Xue
 Publication date 2007
  fields
and research's language is English
 Authors Ting Xue




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We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over $tF_{2^n}$. Let $G$ be an adjoint algebraic group of type $B,C$ or $D$ defined over an algebraically closed field of characteristic 2. We construct the Springer correspondence for the nilpotent variety in the Lie algebra of $G$.



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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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