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
Log
Files
Refs
README
LICENSE

Commit: 41dad6acc9353c9c8929cb6362656e1effdca186
Parent: ca7dc4c8fc87b916bebe3003c113052a5c0f9083
Author: Pablo <pablo-escobar@riseup.net>
Date: Sun, 25 Sep 2022 19:25:42 +0000

Minor change in notation

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
@@ -212,12 +212,12 @@
 \end{proof}
 
 \begin{theorem}[Mathieu]
-  Let \(\mathcal{M}\) be an irreducible coherent family and \(\mu \in
+  Let \(\mathcal{M}\) be an irreducible coherent family and \(\lambda \in
   \mathfrak{h}^*\). The following conditions are equivalent.
   \begin{enumerate}
-    \item \(\mathcal{M}[\mu]\) is irreducible.
-    \item \(F_\alpha\!\restriction_{\mathcal{M}[\mu]}\) is injective for all
+    \item \(\mathcal{M}[\lambda]\) is irreducible.
+    \item \(F_\alpha\!\restriction_{\mathcal{M}[\lambda]}\) is injective for all
       \(\alpha \in \Delta\).
-    \item \(\mathcal{M}[\mu]\) is cuspidal.
+    \item \(\mathcal{M}[\lambda]\) is cuspidal.
   \end{enumerate}
 \end{theorem}