lie-algebras-and-their-representations

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -897,11 +897,11 @@ family are cuspidal representations?
   We claim the set \(U = \{\mu \in \mathfrak{h}^* : \mathcal{M}_\mu \ \text{is
   a simple $\mathcal{U}(\mathfrak{g})_0$-module}\}\) is Zariski-open. If we
   suppose this is the case for a moment or two, it follows from the fact that
-  \(\mathcal{M}\) is simple and \(\operatorname{supp}_{\operatorname{ess}} M\)
-  is Zariski-dense that \(U \cap \operatorname{supp}_{\operatorname{ess}} M\)
-  is non-empty. In other words, there is some \(\mu \in \mathfrak{h}^*\) such
-  that \(\mathcal{M}_\mu\) is a simple \(\mathcal{U}(\mathfrak{g})_0\)-module
-  and \(\dim M_\mu = \deg M\).
+  \(M\) is simple and \(\operatorname{supp}_{\operatorname{ess}} M\) is
+  Zariski-dense that \(U \cap \operatorname{supp}_{\operatorname{ess}} M\) is
+  non-empty. In other words, there is some \(\mu \in \mathfrak{h}^*\) such that
+  \(\mathcal{M}_\mu\) is a simple \(\mathcal{U}(\mathfrak{g})_0\)-module and
+  \(\dim M_\mu = \deg M\).
 
   In particular, \(M_\mu \ne 0\), so \(M_\mu = \mathcal{M}_\mu\). Now given any
   simple \(\mathfrak{g}\)-module \(L\), it follows from