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: af132e871fb6bf2630a04067702f4e0556f8bca1
Parent: 16464140707f877c0dd0c7be5d7a893658819c6d
Author: Pablo <pablo-escobar@riseup.net>
Date: Sun, 11 Sep 2022 23:25:55 +0000

Fixed an error in an equation

Diffstat

1 file changed, 2 insertions, 1 deletion

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/semisimple-algebras.tex	3	2	1

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -2227,7 +2227,8 @@ Moreover, we find\dots
           F_{\alpha_2} \cdots F_{\alpha_n} v^+ \\
       & \;\; \vdots \\
       & = (\alpha_1 + \cdots + \alpha_n)(H) \cdot
-          F_{\alpha_1} \cdots F_{\alpha_n} H v^+ \\
+          F_{\alpha_1} \cdots F_{\alpha_n} v^+
+        + F_{\alpha_1} \cdots F_{\alpha_n} H v^+ \\
       & = (\lambda + \alpha_1 + \cdots + \alpha_n)(H) \cdot
           F_{\alpha_1} \cdots F_{\alpha_n} v^+ \\
       & \therefore F_{\alpha_1} \cdots F_{\alpha_n} v^+