Adjoint Jordan blocks for simple algebraic groups of type Cℓin characteristic two

Let Gbe a simple algebraic group over an algebraically closed field Kwith Lie algebra g. For unipotent elements u∈Gand nilpotent elements e∈g, the Jordan block sizes of Ad(u)and ad(e)are known in most cases. In the cases that remain, the group Gis of classical type in bad characteristic, so charK=2and Gis of type Bℓ,Cℓ, or Dℓ. In this paper, we consider the case where Gis of type Cℓand charK=2. As our main result, we determine the Jordan block sizes of Ad(u)and ad(e)for all unipotent u∈Gand nilpotent e∈g. In the case where Gis of adjoint type, we will also describe the Jordan block sizes on [g,g].