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: b3c896fe830e68f436b43b7d9d9e5244d74c7e28
Parent: 4036d48127438cfd7836526ccab3c931d61f72de
Author: Pablo <pablo-escobar@riseup.net>
Date: Sat, 17 Dec 2022 22:26:31 +0000

Repharased a sentence

Diffstat

1 file changed, 4 insertions, 5 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/semisimple-algebras.tex	9	4	5

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -637,11 +637,10 @@ section.
 
 It is already clear from the previous discussion that if \(\lambda\) is the
 highest weight of \(V\) then \(\lambda(H_\alpha) \ge 0\) for all positive roots
-\(\alpha\). Another way of putting it is to say that having \(\lambda(H_\alpha)
-\ge 0\) for all \(\alpha \in \Delta^+\) is a necessary condition for the
-existence of irreducible representations with highest weight given by
-\(\lambda\). Surprisingly, this condition is also sufficient. In other
-words\dots
+\(\alpha\). In other words, having \(\lambda(H_\alpha) \ge 0\), for all
+\(\alpha \in \Delta^+\), is a necessary condition for the existence of
+irreducible representations with highest weight given by \(\lambda\).
+Surprisingly, this condition is also sufficient. In other words\dots
 
 \begin{definition}
   An element \(\lambda\) of \(P\) such that \(\lambda(H_\alpha) \ge 0\) for all