diff --git a/sections/sl2-sl3.tex b/sections/sl2-sl3.tex
@@ -1,8 +1,5 @@
\chapter{Representations of \(\mathfrak{sl}_2(K)\) and \(\mathfrak{sl}_3(K)\)}
-% TODO: Remove this?
-\epigraph{Nobody has ever bet enough on a winning horse.}{Some gambler}
-
% TODOOOO: Write an intetroduction!
\section{Representations of \(\mathfrak{sl}_2(K)\)}\label{sec:sl2}
@@ -38,11 +35,10 @@ of \(V\) -- where \(\lambda\) ranges over the eigenvalues of \(h\) and
\(V_\lambda\) is the corresponding eigenspace. At this point, this is nothing
short of a gamble: why look at the eigenvalues of \(h\)?
-The short answer is that, as we shall see, this will pay off -- which
-conveniently justifies the epigraph of this chapter. For now we will postpone
-the discussion about the real reason of why we chose \(h\). Let \(\lambda\) be
-any eigenvalue of \(h\). Notice \(V_\lambda\) is in general not a
-subrepresentation of \(V\). Indeed, if \(v \in V_\lambda\) then
+The short answer is that, as we shall see, this will pay off. For now we will
+postpone the discussion about the real reason of why we chose \(h\). Let
+\(\lambda\) be any eigenvalue of \(h\). Notice \(V_\lambda\) is in general not
+a subrepresentation of \(V\). Indeed, if \(v \in V_\lambda\) then
\begin{align*}
h e v & = 2e v + e h v = (\lambda + 2) e v \\
h f v & = - 2f v + f h v = (\lambda - 2) f v