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
f72a9a6c98cd1c4f1c1cdf71134b8aeae10d6b4f
Parent
3fa78459f8f579064cee9408d75c40d70112ed32
Author
Pablo <pablo-escobar@riseup.net>
Date

Added a TODO item

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1 file changed, 1 insertion, 0 deletions

Status File Name N° Changes Insertions Deletions
Modified sections/semisimple-algebras.tex 1 1 0 
diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -701,6 +701,7 @@ Moreover, we find\dots
   \(M(\lambda)\) have the form \(\mu = \lambda + k_1 \cdot \alpha_1 + \cdots +
   k_n \cdot \alpha_n\).
 
+  % TODO: Note that PBW implies U(g) is a free b-module
   This already gives us that the weights of \(M(\lambda)\) are bounded by
   \(\lambda\) -- in the sense that no weight of \(M(\lambda)\) is ``higher''
   than \(\lambda\). To see that \(\lambda\) is indeed a weight, we show that