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

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1 file changed, 10 insertions, 1 deletion

diff --git a/TODO.md b/TODO.md
@@ -1,6 +1,15 @@
 # TODO
 
-* Prove the existance of Mathieu's Ext coherent extension
+* Prove the uniqueness of Mathieu's Ext coherent extension
+  * Prove that the essential support is Zariski-dense (I don't think this proof
+    is worth it)
+  * Prove that the weight spaces of a simple admissible 𝔤-module is a simple
+    module over the centralizer of 𝔥 (Is this proof worth it?)
+  * Prove that the multiplicity of a simple module L in a completely reducible
+    weight module is the same as the multiplicity of L_λ in the weight space of
+    λ (Is this proof worth it?)
+  * Prove that a completely-reducible weight-module is determined by its trace
+    function
 * Prove Mathieu's classification of which submodules of a coherent family are
   simple and cuspidal