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: d06a7808deb4c48b79fc009e855ef0d2405737ea
Parent: ec9370a1bdb7259ffccf834b4ef5309b5623f853
Author: Pablo <pablo-escobar@riseup.net>
Date: Wed, 28 Dec 2022 22:24:41 +0000

Fixed a typo

Diffstat

1 file changed, 1 insertion, 1 deletion

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

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -702,7 +702,7 @@ known as \emph{Verma modules}.
   The \(\mathfrak{g}\)-module \(M(\lambda) =
   \operatorname{Ind}_{\mathfrak{b}}^{\mathfrak{g}} K m^+\), where the action of
   \(\mathfrak{b}\) on \(K m^+\) is given by \(H \cdot m^+ = \lambda(H) m^+\)
-  for all \(H \in \mathfrak{h}\) and \(X \cdot v^+ = 0\) for \(X \in
+  for all \(H \in \mathfrak{h}\) and \(X \cdot m^+ = 0\) for \(X \in
   \mathfrak{g}_{\alpha}\), \(\alpha \in \Delta^+\), is called \emph{the Verma
   module of weight \(\lambda\)}.
 \end{definition}