lie-algebras-and-their-representations

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -637,11 +637,10 @@ section.
 
 It is already clear from the previous discussion that if \(\lambda\) is the
 highest weight of \(V\) then \(\lambda(H_\alpha) \ge 0\) for all positive roots
-\(\alpha\). Another way of putting it is to say that having \(\lambda(H_\alpha)
-\ge 0\) for all \(\alpha \in \Delta^+\) is a necessary condition for the
-existence of irreducible representations with highest weight given by
-\(\lambda\). Surprisingly, this condition is also sufficient. In other
-words\dots
+\(\alpha\). In other words, having \(\lambda(H_\alpha) \ge 0\), for all
+\(\alpha \in \Delta^+\), is a necessary condition for the existence of
+irreducible representations with highest weight given by \(\lambda\).
+Surprisingly, this condition is also sufficient. In other words\dots
 
 \begin{definition}
   An element \(\lambda\) of \(P\) such that \(\lambda(H_\alpha) \ge 0\) for all