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: 5b5fa38509febcf637282a433a53ace793246e29
Parent: 51e9c3007ff31a835c1a6bfe39bdb8aac2251db1
Author: Pablo <pablo-escobar@riseup.net>
Date: Sun, 13 Nov 2022 20:37:04 +0000

Removed an unnecessary theorem

Diffstat

1 file changed, 9 insertions, 4 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/mathieu.tex	13	9	4

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -1218,7 +1218,12 @@ To finish the proof, we now show\dots
   \(\operatorname{Ext}(V)\) is unique.
 \end{proof}
 
-\begin{proposition}[Mathieu]
-  The central characters of the irreducible submodules of
-  \(\operatorname{Ext}(V)\) are all the same.
-\end{proposition}
+% TODO: Remove this
+% This is a very important theorem, but since we won't classify the coherent
+% extensions in here we don't need it, and there is no other motivation behind
+% it. Including this would also require me to explain what central characters
+% are, which is a bit of a pain
+%\begin{proposition}[Mathieu]
+%  The central characters of the irreducible submodules of
+%  \(\operatorname{Ext}(V)\) are all the same.
+%\end{proposition}