Adjoint Jordan blocks for simple algebraic groups of type Cℓ in characteristic two

Let G be a simple algebraic group over an algebraically closed field K with Lie algebra g. For unipotent elements u is an element of G and nilpotent elements e is an element of g, the Jordan block sizes of Ad(u) and ad(e) are known in most cases. In the cases that remain, the group G is of classical type in bad characteristic, so char K = 2 and G is of type B-l, C-l, or Dt. In this paper, we consider the case where G is of type C-l and char K = 2. As our main result, we determine the Jordan block sizes of Ad(u) and ad(e) for all unipotent u is an element of G and nilpotent e is an element of g. In the case where G is of adjoint type, we will also describe the Jordan block sizes on [g, g].