lie-algebras-and-their-representations

Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules

Diffstat

1 file changed, 6 insertions, 4 deletions

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -210,10 +210,12 @@ clear things up.
   choice of \(j\), it then follows \(V = W \oplus U\).
 \end{proof}
 
-The advantage of working with irreducible representations as opposed to
-indecomposable ones is that they are generally much easier to find. The
-relationship between irreducible representations is also well understood. This
-is because of the following result, known as \emph{Schur's Lemma}.
+While are primarily interested in indecomposable representations -- which is
+usually a strickly larger class of representations than that of irreducible
+representations -- it is important to note that irreducible representations are
+generally much easier to find. The relationship between irreducible
+representations is also well understood. This is because of the following
+result, known as \emph{Schur's Lemma}.
 
 \begin{lemma}[Schur]
   Let \(V\) and \(W\) be irreducible representations of \(\mathfrak{g}\) and