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

Details Nilpotent orbits in classical Lie algebras over $F_{2^n}$ and the Springer correspondence Nilpotent orbits in classical Lie algebras over $F_{2^n}$ and the Springer correspondence

2008-08-21

arxiv.org/abs/0808.2995v2

Mathematics

Representation Theory

17 pages

Scientific paper

10.1073/pnas.0709626104

We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over $\tF_{2^n}$. We also obtain the structure of 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 Lie algebra of $G$.

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