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

Diffstat

1 file changed, 3 insertions, 2 deletions

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -2249,8 +2249,9 @@ Moreover, we find\dots
   k_n \cdot \alpha_n\).
 
   This already gives us that the weights of \(M(\lambda)\) are bounded by
-  \(\lambda\). To see that \(\lambda\) is indeed a weight, we show that \(v^+\)
-  is nonzero weight vector. Clearly \(v^+ \in V_\lambda\). The
+  \(\lambda\) -- in the sence that no weight of \(M(\lambda)\) is ``higher''
+  than \(\lambda\). To see that \(\lambda\) is indeed a weight, we show that
+  \(v^+\) is nonzero weight vector. Clearly \(v^+ \in V_\lambda\). The
   Poincaré-Birkhoff-Witt theorem implies
   \[
     M(\lambda)