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: 9b394c58f19539bef0e02d417f436b1a14d34dae
Parent: af132e871fb6bf2630a04067702f4e0556f8bca1
Author: Pablo <pablo-escobar@riseup.net>
Date: Sun, 11 Sep 2022 23:29:03 +0000

Added some clarification on language

Diffstat

1 file changed, 3 insertions, 2 deletions

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

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -2249,8 +2249,9 @@ Moreover, we find\dots
   k_n \cdot \alpha_n\).
 
   This already gives us that the weights of \(M(\lambda)\) are bounded by
-  \(\lambda\). To see that \(\lambda\) is indeed a weight, we show that \(v^+\)
-  is nonzero weight vector. Clearly \(v^+ \in V_\lambda\). The
+  \(\lambda\) -- in the sence that no weight of \(M(\lambda)\) is ``higher''
+  than \(\lambda\). To see that \(\lambda\) is indeed a weight, we show that
+  \(v^+\) is nonzero weight vector. Clearly \(v^+ \in V_\lambda\). The
   Poincaré-Birkhoff-Witt theorem implies
   \[
     M(\lambda)