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: 28f2e249c64ccaee5d2692e30257f4879281f4cd
Parent: 04fa43522b0153f4f609d1909f2b9eaa8ba34532
Author: Pablo <pablo-escobar@riseup.net>
Date: Mon, 14 Nov 2022 18:33:57 +0000

Removed some footnotes

Diffstat

1 file changed, 6 insertions, 6 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/mathieu.tex	12	6	6

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -314,13 +314,13 @@ characterizations of cuspidal modules.
   Let \(V\) be an irreducible weight \(\mathfrak{g}\)-module. The following
   conditions are equivalent.
   \begin{enumerate}
-    \item \(V\) is cuspidal.
-    \item \(F_\alpha\) acts injectively\footnote{This is what's usually refered
-      to as a \emph{dense} representation in the literature.} in \(V\) for all
-      \(\alpha \in \Delta\).
-    \item The support of \(V\) is precisely one \(Q\)-coset\footnote{This is
+    \item \(V\) is cuspidal
+    \item \(F_\alpha\) acts injectively in \(V\) for all
+      \(\alpha \in \Delta\) -- this is what's usually refered
+      to as a \emph{dense} representation in the literature
+    \item The support of \(V\) is precisely one \(Q\)-coset -- this is
       what's usually referred to as a \emph{torsion-free} representation in the
-      literature.}.
+      literature
   \end{enumerate}
 \end{corollary}