Let G be a simple algebraic group over an algebraically closed field K with Lie algebra g\documentclass[12pt]{minimal}
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\begin{document}$${\mathfrak {g}}$$\end{document}. For unipotent elements u∈G\documentclass[12pt]{minimal}
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\begin{document}$$u \in G$$\end{document} and nilpotent elements e∈g\documentclass[12pt]{minimal}
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\begin{document}$$e \in {\mathfrak {g}}$$\end{document}, the Jordan block sizes of Ad(u)\documentclass[12pt]{minimal}
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\begin{document}$${\text {Ad}}\hspace{0.55542pt}(u)$$\end{document} and ad(e)\documentclass[12pt]{minimal}
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\begin{document}$${\text {ad}}\hspace{0.55542pt}(e)$$\end{document} are known in most cases. In the cases that remain, the group G is of classical type in bad characteristic, so charK=2\documentclass[12pt]{minimal}
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\begin{document}$${\text {char}} K = 2$$\end{document} and G is of type Bℓ,Cℓ\documentclass[12pt]{minimal}
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\begin{document}$$B_{\ell }, C_{\ell }$$\end{document}, or Dℓ\documentclass[12pt]{minimal}
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\begin{document}$$D_{\ell }$$\end{document}. In this paper, we consider the case where G is of type Cℓ\documentclass[12pt]{minimal}
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\begin{document}$$C_{\ell }$$\end{document} and charK=2\documentclass[12pt]{minimal}
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\begin{document}$${\text {char}} K = 2$$\end{document}. As our main result, we determine the Jordan block sizes of Ad(u)\documentclass[12pt]{minimal}
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\begin{document}$${\text {Ad}}\hspace{0.55542pt}(u)$$\end{document} and ad(e)\documentclass[12pt]{minimal}
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\begin{document}$${\text {ad}}\hspace{0.55542pt}(e)$$\end{document} for all unipotent u∈G\documentclass[12pt]{minimal}
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\begin{document}$$u \in G$$\end{document} and nilpotent e∈g\documentclass[12pt]{minimal}
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\begin{document}$$e \in {\mathfrak {g}}$$\end{document}. In the case where G is of adjoint type, we will also describe the Jordan block sizes on [g,g]\documentclass[12pt]{minimal}
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\begin{document}$$[{\mathfrak {g}}, {\mathfrak {g}}]$$\end{document}.
