lie-algebras-and-their-representations

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -16,17 +16,14 @@ semisimple case. For this reason, we will focus exclusively on the
 classification of completely reducible representations. Our strategy is, once
 again, to classify the irreducible representations.
 
-% TODO: Add references to the motivation
 Secondly, and this is more important, we now consider
-\emph{infinite-dimensional} representations too. The motivation behind looking
-at infinite-dimensional modules was already explained in the introduction, but
-this introduces numerous complications to our analysis. For example, if
-\(\mathcal{U}(\mathfrak{g})\) is the regular \(\mathfrak{g}\)-module then
-\(\mathcal{U}(\mathfrak{g})_\lambda = 0\) for all \(\lambda \in
-\mathfrak{h}^*\). This follows from the fact that \(\mathcal{U}(\mathfrak{g})\)
-has no zero divisors: given \(u \in \mathcal{U}(\mathfrak{g})\), \((H -
-\lambda(H)) u = 0\) for some nonzero \(H \in \mathfrak{h}\) implies \(u = 0\).
-In particular,
+\emph{infinite-dimensional} representations too, which introduces numerous
+complications to our analysis. For example, if \(\mathcal{U}(\mathfrak{g})\) is
+the regular \(\mathfrak{g}\)-module then \(\mathcal{U}(\mathfrak{g})_\lambda =
+0\) for all \(\lambda \in \mathfrak{h}^*\). This follows from the fact that
+\(\mathcal{U}(\mathfrak{g})\) has no zero divisors: given \(u \in
+\mathcal{U}(\mathfrak{g})\), \((H - \lambda(H)) u = 0\) for some nonzero \(H
+\in \mathfrak{h}\) implies \(u = 0\). In particular,
 \[
   \bigoplus_\lambda \mathcal{U}(\mathfrak{g})_\lambda
   = 0