Nilpotent orbits in classical Lie algebras over finite fields of characteristic 2 and the Springer correspondence

Abstract

Let G G be an adjoint algebraic group of type B B , C C , or D D over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the Lie algebra of G 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.