diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -792,8 +792,6 @@ Moreover, we find\dots
\end{align*}
In the language of the diagrams used in chapter~\ref{ch:sl3}, we write
- % TODO: Add a label to the righ of the diagram indicating that the top arrows
- % are the action of e and the bottom arrows are the action of f
\begin{center}
\begin{tikzcd}
\cdots \arrow[bend left=60]{r}{-10}
@@ -804,9 +802,10 @@ Moreover, we find\dots
& M(\lambda)_2 \arrow[bend left=60]{l}{1}
\end{tikzcd}
\end{center}
- where \(M(\lambda)_{2 - 2 k} = K f^k v\). In this case, unlike we have see in
- chapter~\ref{ch:sl3}, the string of weight spaces to left of the diagram is
- infinite.
+ where \(M(\lambda)_{2 - 2 k} = K f^k v\). Here the top arrows represent the
+ action of \(e\) and the bottom arrows represent the action of \(f\). In this
+ case, unlike we have see in chapter~\ref{ch:sl3}, the string of weight spaces
+ to left of the diagram is infinite.
\end{example}
What's interesting to us about all this is that we've just constructed a