lie-algebras-and-their-representations

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -619,7 +619,7 @@ Moreover, we find\dots
     f^{k + 1} v^+ & \overset{h}{\mapsto} - 2 k f^{k + 1} v^+ &
   \end{align*}
 
-  In the language of the diagrams used in section~\ref{sec:sl2}, we write
+  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}
@@ -633,7 +633,7 @@ Moreover, we find\dots
     \end{tikzcd}
   \end{center}
   where \(M(\lambda)_{2 - 2 k} = K f^k v\). In this case, unlike we have see in
-  section~\ref{sec:sl2}, the string of weight spaces to left of the diagram is
+  chapter~\ref{ch:sl3}, the string of weight spaces to left of the diagram is
   infinite.
 \end{example}
 
@@ -708,7 +708,7 @@ whose highest weight is \(\lambda\).
   3} K f^k v^+\), so that \(\sfrac{M(\lambda)}{N(\lambda)}\) is the
   \(3\)-dimensional irreducible representation of \(\mathfrak{sl}_2(K)\) --
   i.e. the finite-dimensional irreducible representation with highest weight
-  \(\lambda\) constructed in section~\ref{sec:sl2}.
+  \(\lambda\) constructed in chapter~\ref{ch:sl3}.
 \end{example}
 
 This last example is particularly interesting to us, since it indicates that

diff --git a/sections/sl2-sl3.tex b/sections/sl2-sl3.tex
@@ -1,9 +1,7 @@
-\chapter{Representations of \(\mathfrak{sl}_2(K)\) and \(\mathfrak{sl}_3(K)\)}
+\chapter{Representations of \(\mathfrak{sl}_3(K)\)}\label{ch:sl3}
 
 % TODOOOO: Write an intetroduction!
 
-\section{Representations of \(\mathfrak{sl}_2(K)\)}\label{sec:sl2}
-
 The primary goal of this section is proving\dots
 
 \begin{theorem}\label{thm:sl2-exist-unique}
@@ -263,7 +261,7 @@ will \emph{somehow} lead us to a general solution. In the process of doing so
 we'll learn a bit more why \(h\) was a sure bet and the race was fixed all
 along.
 
-\section{Representations of \(\mathfrak{sl}_3(K)\)}\label{sec:sl3-reps}
+\section{Representations of \(\mathfrak{sl}_{2 + 1}(K)\)}\label{sec:sl3-reps}
 
 The study of representations of \(\mathfrak{sl}_2(K)\) reminds me of the
 difference the derivative of a function \(\RR \to \RR\) and that of a smooth