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: c944e8c3946fdde771366101c59c4b52511a52a9
Parent: 0cda277464d901b72135fb7e2f092c3c41d1a6c0
Author: Pablo <pablo-escobar@riseup.net>
Date: Mon, 26 Sep 2022 14:26:16 +0000

Added a description of the weight spaces of a subrepresentation of a weight module

Diffstat

1 file changed, 3 insertions, 2 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/mathieu.tex	5	3	2

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -26,8 +26,9 @@
   proposition~\ref{thm:max-verma-submod-is-weight} imply that the Verma module
   \(M(\lambda)\) and its maximal subrepresentation are both weight modules. In
   fact, the proof of proposition~\ref{thm:max-verma-submod-is-weight} is
-  actually a proof of the fact that every subrepresentation of a weight module
-  is a weight module.
+  actually a proof of the fact that every subrepresentation \(W \subset V\) of
+  a weight module \(V\) is a weight module, and \(W_\lambda = V_\lambda \cap
+  W\) for all \(\lambda \in \mathfrak{h}^*\).
 \end{example}
 
 \begin{example}