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
Log
Files
Refs
README
LICENSE

Commit: 09fea928cc0a047acfe95545325b75d75a14d0a9
Parent: 20117e2e20c0f2eb66b41e4a837fcf5e33ce02ba
Author: Pablo <pablo-escobar@riseup.net>
Date: Sat, 10 Jun 2023 14:41:59 +0000

Minor tweak in notation

Diffstat

1 file changed, 3 insertions, 3 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/simple-weight.tex	6	3	3

diff --git a/sections/simple-weight.tex b/sections/simple-weight.tex
@@ -109,8 +109,8 @@ to the case it holds. This brings us to the following definition.
     (M_1 \otimes M_2)_{\lambda_1 + \lambda_2}
     = (M_1)_{\lambda_1} \otimes (M_2)_{\lambda_2}
   \]
-  for all \(\lambda_i \in \mathfrak{h}_i^*\) and \(\operatorname{supp} M_1
-  \otimes M_2 = \operatorname{supp} M_1 \oplus \operatorname{supp} M_2 = \{
+  for all \(\lambda_i \in \mathfrak{h}_i^*\) and \(\operatorname{supp} (M_1
+  \otimes M_2) = \operatorname{supp} M_1 \oplus \operatorname{supp} M_2 = \{
   \lambda_1 + \lambda_2 : \lambda_i \in \operatorname{supp} M_i \subset
   \mathfrak{h}_i^*\}\).
 \end{example}
@@ -184,7 +184,7 @@ A particularly well behaved class of examples are the so called
   a bounded \(\mathfrak{g}\)-module with \(\deg M_1 \otimes M_2 = \deg M_1
   \cdot \deg M_2\) and
   \[
-    \operatorname{supp}_{\operatorname{ess}} M_1 \otimes M_2
+    \operatorname{supp}_{\operatorname{ess}} (M_1 \otimes M_2)
     = \operatorname{supp}_{\operatorname{ess}} M_1 \oplus
       \operatorname{supp}_{\operatorname{ess}} M_2
     = \{