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

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

2008-08-21

arxiv.org/abs/0808.2998v1

Mathematics

Representation Theory

19 pages

Scientific paper

We classify the nilpotent orbits in the dual space of the classical Lie algebras over an algebraically closed field or a finite field of characteristic 2. In particular, we obtain the number of nilpotent orbits over $\tF_{2^n}$. We also give the structure of the component groups of centralizers. 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 dual space of the Lie algebra of $G$.

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