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

TL;DR

This paper constructs a Springer correspondence for the dual of classical Lie algebras in characteristic 2, classifying nilpotent orbits in symplectic and orthogonal cases over algebraically closed fields.

Contribution

It develops a Springer correspondence in characteristic 2 and classifies nilpotent orbits in the duals of classical Lie algebras, extending previous theories.

Findings

Classified nilpotent orbits in duals of symplectic and orthogonal Lie algebras in characteristic 2.

Constructed a Springer correspondence for these dual spaces.

Extended the understanding of nilpotent orbits and Springer correspondence to characteristic 2.

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.