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: d89fdc9c1c66a64e5dff3b79d344fdbc0683c97d
Parent: d485955b90bfe5f191dff4cc958d34fe18e08cd4
Author: Pablo <pablo-escobar@riseup.net>
Date: Wed, 9 Nov 2022 21:08:19 +0000

Edited some TODO items

Diffstat

1 file changed, 2 insertions, 2 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/mathieu.tex	4	2	2

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -60,7 +60,7 @@
 
 % TODO: Add an example of a module wich is NOT a weight module
 
-% TODOO: Prove this?
+% TODOO: Prove this? Most likely not!
 \begin{proposition}\label{thm:centralizer-multiplicity}
   Let \(V\) be a completely reducible weight \(\mathfrak{g}\)-module. Then
   \(V_\lambda\) is a semisimple
@@ -120,7 +120,7 @@
   which is \emph{not} parabolic induced.
 \end{definition}
 
-% TODOO: w should be an element of the subgroup W(V) of W. Fix this!
+% TODOOO: w should be an element of the subgroup W(V) of W. Fix this!
 % TODO: Remark on the fact that any simple weight p-mod is a (p/u)-mod, so that
 % the notation of a cuspidal p-mod is well definited
 % TODO: Define the conjugation of a p-mod by an element of the Weil group