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: 4036d48127438cfd7836526ccab3c931d61f72de
Parent: 65d40132357293d350dbc94eaa9608046ee045f6
Author: Pablo <pablo-escobar@riseup.net>
Date: Sat, 17 Dec 2022 22:24:38 +0000

Changed a single word

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
@@ -491,7 +491,7 @@ order. In addition, we may compare the elements of a given \(Q\)-coset
 \(\lambda + Q\) by comparing their difference with \(0 \in Q\). In other words,
 given \(\lambda \in \mu + Q\), we say \(\lambda \preceq \mu\) if \(\lambda -
 \mu \preceq 0\). In particular, since the weights of \(V\) all lie in a single
-\(Q\)-coset, we may compare them in this fashion. Given a basis \(\Sigma\) for
+\(Q\)-coset, we may compare them in this way. Given a basis \(\Sigma\) for
 \(\Delta\) we may take ``the highest weight of \(V\)'' as a maximal weight
 \(\lambda\) of \(V\). The obvious question then is: can we always find a basis
 for \(\Delta\)?