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: 491346ac0d57fd72dd8538362dde464788b16ee4
Parent: 04151543ab7cc7c234dbdc2f73acad263e22aa31
Author: Pablo <pablo-escobar@riseup.net>
Date: Wed, 28 Dec 2022 21:24:57 +0000

Fixed some typos

Diffstat

1 file changed, 2 insertions, 2 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/complete-reducibility.tex	4	2	2

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -721,7 +721,7 @@ establish\dots
   % because the action of every element of g is strictly upper triangular -- and
   % semisimple -- because it is a quotient of g, which is semisimple. We thus
   % have rho(g) = 0, so that W is trivial
-  Since \(\dim W = 2\), the simple component \(\mathcal{U}(\mathfrak{g})
+  Since \(\dim N = 2\), the simple component \(\mathcal{U}(\mathfrak{g})
   \cdot n\) of \(n\) in \(N\) is either \(K n\) or \(N\) itself. But this
   component cannot be \(N\), since the image of \(f\) is a
   \(1\)-dimensional \(\mathfrak{g}\)-module -- i.e. a proper nonzero submodule.
@@ -743,7 +743,7 @@ establish\dots
   such that
   \[
     0
-    = (C_V - \lambda)^r \cdot n
+    = (C_M - \lambda)^r \cdot n
     = \sum_{k = 0}^r (-1)^k \binom{r}{k} \lambda^k C_M^{r - k} \cdot n
   \]
   for some \(r \ge 1\).