lie-algebras-and-their-representations

diff --git a/sections/sl2-sl3.tex b/sections/sl2-sl3.tex
@@ -584,6 +584,9 @@ implemented for \(\mathfrak{sl}_3(K)\) -- and indeed that's what we'll do later
 down the line -- but instead we would like to focus on the problem of finding
 the weights of \(V\) for the moment.
 
+% TODO: Move this to before showing V is a highest weight module
+% TODO: This would allow us to justify drawing the weight diagrams in the real
+% plane as opposed to some abstract 4-dimensional space
 We'll start out by trying to understand the weights in the boundary of
 \(\frac{1}{3}\)-plane previously drawn. Since the root spaces act by
 translation, the action of \(E_{2 1}\) in \(V_\lambda\) will span a subspace
@@ -811,6 +814,9 @@ must also be weights of \(V\). The final picture is thus
   \end{tikzpicture}
 \end{center}
 
+% TODO: Move this to just after the discussion on the distinguished subalgebras
+% TODO: This would allow us to justify the fact we've been drawing the highest
+% weight of V as an element of the weight lattice
 Another important consequence of our analysis is the fact that \(\lambda\) lies
 in the lattice \(P\) generated by \(\alpha_1\), \(\alpha_2\) and \(\alpha_3\).
 Indeed, \(\lambda([E_{i j}, E_{j i}])\) is an eigenvalue of \(h\) in a