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

git clone: git://git.pablopie.xyz/lie-algebras-and-their-representations
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Commit: 09bbf643742c75fee40c6e0db1d1e5817a9359ae
Parent: 1d71b805f37105f3a65c615550f3ad2fe849febb
Author: Pablo <pablo-escobar@riseup.net>
Date: Thu, 29 Dec 2022 12:23:54 +0000

Fixed some typos

Added missing periods

Diffstat

1 file changed, 4 insertions, 4 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/mathieu.tex	8	4	4

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -307,13 +307,13 @@ characterizations of cuspidal modules.
   Let \(M\) be a simple weight \(\mathfrak{g}\)-module. The following
   conditions are equivalent.
   \begin{enumerate}
-    \item \(M\) is cuspidal
+    \item \(M\) is cuspidal.
     \item \(F_\alpha\) acts injectively on \(M\) for all
       \(\alpha \in \Delta\) -- this is what is usually referred
-      to as a \emph{dense} module in the literature
+      to as a \emph{dense} module in the literature.
     \item The support of \(M\) is precisely one \(Q\)-coset -- this is
       what is usually referred to as a \emph{torsion-free} module in the
-      literature
+      literature.
   \end{enumerate}
 \end{corollary}
 
@@ -446,7 +446,7 @@ families}.
   \begin{enumerate}
     \item \(\dim \mathcal{M}_\lambda = d\) for \emph{all} \(\lambda \in
       \mathfrak{h}^*\) -- i.e. \(\operatorname{supp}_{\operatorname{ess}}
-      \mathcal{M} = \mathfrak{h}^*\)
+      \mathcal{M} = \mathfrak{h}^*\).
     \item For any \(u \in \mathcal{U}(\mathfrak{g})\) in the
       centralizer\footnote{The notation $\mathcal{U}(\mathfrak{g})_0$ for the
       centralizer of $\mathfrak{h}$ in $\mathcal{U}(\mathfrak{g})$ comes from