lie-algebras-and-their-representations

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -152,11 +152,11 @@ A particularly well behaved class of examples are the so called
 Notice that the support of \(K[x, x^{-1}]\) is the trivial \(2
 \mathbb{Z}\)-coset \(0 + 2 \mathbb{Z}\). This is representative of the general
 behavious in the following sense: if \(V\) is an irreducible weight
-\(\mathfrak{g}\)-module, since \(\bigoplus_{\alpha \in Q} V_{\lambda +
-\alpha}\) is stable under the action of \(\mathfrak{g}\) for all \(\lambda \in
-\mathfrak{h}^*\), \(\bigoplus_{\alpha \in Q} V_{\lambda + \alpha}\) is either
-\(0\) or all \(V\). In other words, the support of an irreducible weight module
-is allways contained in a single \(Q\)-coset.
+\(\mathfrak{g}\)-module, since \(V[\lambda] = \bigoplus_{\alpha \in Q}
+V_{\lambda + \alpha}\) is stable under the action of \(\mathfrak{g}\) for all
+\(\lambda \in \mathfrak{h}^*\), \(\bigoplus_{\alpha \in Q} V_{\lambda +
+\alpha}\) is either \(0\) or all \(V\). In other words, the support of an
+irreducible weight module is allways contained in a single \(Q\)-coset.
 
 However, the behaviour of \(K[x, x^{-1}]\) deviates from that of an arbitrary
 admissible representation in the sence its essential support is precisely the