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
Log
Files
Refs
README
LICENSE

Commit: 498abf26b9e1049aea20337e8ba0f2169d9641e4
Parent: 271ee36062a38d669ece51f86a26fd661a75d01a
Author: Pablo <pablo-escobar@riseup.net>
Date: Thu, 1 Dec 2022 13:11:14 +0000

Minor tweak in language

Diffstat

1 file changed, 3 insertions, 3 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/sl2-sl3.tex	6	3	3

diff --git a/sections/sl2-sl3.tex b/sections/sl2-sl3.tex
@@ -706,7 +706,7 @@ multiple choices the ``weight lying the furthest'' along this direction.
 \end{definition}
 
 The next observation we make is that all others weights of \(V\) must lie in a
-sort of \(\frac{1}{3}\)-plane with corners at \(\lambda\), as shown in
+sort of \(\frac{1}{3}\)-cone with apex at \(\lambda\), as shown in
 \begin{center}
   \begin{tikzpicture}
     \AutoSizeWeightLatticefalse
@@ -756,8 +756,8 @@ down the line -- but instead we would like to focus on the problem of finding
 the weights of \(V\) in the first place.
 
 We'll start out by trying to understand the weights in the boundary of
-\(\frac{1}{3}\)-plane previously drawn. As we've just seen, we can get to other
-weight spaces from \(V_\lambda\) by successively applying \(E_{2 1}\).
+previously drawn cone. As we've just seen, we can get to other weight spaces
+from \(V_\lambda\) by successively applying \(E_{2 1}\).
 \begin{center}
   \begin{tikzpicture}
     \begin{rootSystem}{A}