Nilpotent orbits in classical Lie algebras over F2n and the Springer correspondence

We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over F-2n. 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.