diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -279,7 +279,7 @@
\begin{corollary}
Let \(\Sigma\) be as in lemma~\ref{thm:nice-basis-for-inversion} and
\((F_\alpha : \alpha \in \Sigma) \subset \mathcal{U}(\mathfrak{g})\) be
- the multiplicative subset generated by \(F_\alpha\), \(\alpha \in F_\alpha\).
+ the multiplicative subset generated by \(F_\alpha\), \(\alpha \in \Sigma\).
The \(K\)-algebra \(\mathcal{U}(\mathfrak{g})_{(F_\alpha : \alpha \in
\Sigma)}\) is well defined and the localization map
\begin{align*}
@@ -341,6 +341,7 @@
\(\operatorname{Ext}(V)\) is irreducible as a coherent family.
\end{theorem}
+% TODOOO: Prove the uniqueness
\begin{proof}
The existence part should now be clear from the previous discussion: let
\(\Lambda\) be a set of representatives of the \(Q\)-cosets in
@@ -381,7 +382,7 @@
\subset \operatorname{Ext}(V)
\]
- % TODOO: Prove that the weight spaces of any simple g-module are all simple
+ % TODOOO: Prove that the weight spaces of any simple g-module are all simple
% C(h)-modules
Since the degree of \(V\) is the same as the degree of
\(\operatorname{Ext}(V)\), some of its weight spaces have maximal dimension
@@ -390,8 +391,6 @@
a simple \(C_{\mathcal{U}(\mathfrak{h})}(\mathfrak{h})\)-module for some
\(\lambda \in \operatorname{supp} V\), so that \(\operatorname{Ext}(V)\) is
irreducible as a coherent family.
-
- % TODOO: Prove the uniqueness
\end{proof}
\begin{proposition}[Mathieu]