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: 20117e2e20c0f2eb66b41e4a837fcf5e33ce02ba
Parent: 6b75623635f9613c22bb72584f71e7a877e71474
Author: Pablo <pablo-escobar@riseup.net>
Date: Fri, 9 Jun 2023 22:08:49 +0000

Fixed a small typo

Fixed a typo regarding the order relation on Q

Diffstat

1 file changed, 1 insertion, 2 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/fin-dim-simple.tex	3	1	2

diff --git a/sections/fin-dim-simple.tex b/sections/fin-dim-simple.tex
@@ -520,8 +520,7 @@ induces an order in \(Q\), where elements are ordered by their
   \emph{parabolic} if \(\mathfrak{p} \supset \mathfrak{b}\).
 \end{definition}
 
-% TODO: This is a total order on Q, not a partial order
-It should be obvious that the binary relation \(\preceq\) in \(Q\) is a partial
+It should be obvious that the binary relation \(\preceq\) in \(Q\) is a total
 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 -