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

Commit
f9133eab0004eedb3be169e1ea72a3a5993c80f8
Parent
a3e69f1fe63270514bda5a81e1f10c7754c26b18
Author
Pablo <pablo-escobar@riseup.net>
Date

Fixed a typo

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
@@ -531,7 +531,7 @@ establish\dots
 
   Now suppose that \(V\) is non-trivial, so that \(C_V\) acts on \(V\) as
   \(\lambda \operatorname{Id}\) for some \(\lambda \ne 0\). Given an eigenvalue
-  \(\mu \in K\) of the action of \(C\) in \(W\), denote by \(W^\mu\) its
+  \(\mu \in K\) of the action of \(C_V\) in \(W\), denote by \(W^\mu\) its
   associated generalized eigenspace. We claim \(W^0\) is the image of the
   inclusion \(K \to W\). Since \(C_V\) acts as zero in \(K\), this image is
   clearly contained in \(W^0\). On the other hand, if \(w \in W\) is such that