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: f4df5a41622960746aaf11ba08795d47e59f00ca
Parent: f2b649f66c75aba0a70f1b5c7ab19f258edc6866
Author: Pablo <pablo-escobar@riseup.net>
Date: Thu, 16 Mar 2023 16:46:00 +0000

Fixed a typo

Diffstat

1 file changed, 1 insertion, 1 deletion

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/mathieu.tex	2	1	1

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -841,7 +841,7 @@ deemed informative enough to be included in here, but see the proof of Lemma
     \bigcup_{\substack{V \subset \mathcal{U}(\mathfrak{g})_0 \\ \dim V = d}}
     U_V,
   \]
-  where \(U_V = \{\lambda \in \mathcal{U}(\mathfrak{g})_0 : \operatorname{rank}
+  where \(U_V = \{\lambda \in \mathfrak{h}^* : \operatorname{rank}
   B_\lambda\!\restriction_V = d^2 \}\). Here \(V\) ranges over all
   \(d\)-dimensional subspaces of \(\mathcal{U}(\mathfrak{g})_0\) -- \(V\) is
   not necessarily a \(\mathcal{U}(\mathfrak{g})_0\)-submodule.