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
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Commit: 5022a6834593ce27761628563bcafe4eaa0c618d
Parent: fa77efc8dfa5dbab55b3ce7fe1c6cbc202aef6de
Author: Pablo <pablo-escobar@riseup.net>
Date: Mon, 14 Nov 2022 19:34:35 +0000

Updated the TODO list

Diffstat

1 file changed, 9 insertions, 14 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	TODO.md	23	9	14

diff --git a/TODO.md b/TODO.md
@@ -1,19 +1,14 @@
 # TODO
 
-* Prove Mathieu's classification of which submodules of a coherent family are
-  simple and cuspidal
-* 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?
-* Prove that the weight spaces of a simple admissible 𝔤-module is a simple
-  module over the centralizer of 𝔥?
-
-* Make a proper discussion on basis
-* Make a proper discussion of highest weight modules
 * Write something on the motivation for the representation theory of Lie
   algebras
-  * Main motivation: smooth representations of Lie groups and rational
-    representations of algebraic groups
-  * This also serves as motivation for infinite-dimensional representations:
-    the work of Vogan on the relationship between unitary representations of
+  * Smooth representations of Lie groups and rational representations of
+    algebraic groups
+  * The geometric realization of the universal enveloping algebra and D-modules
+  * The work of Vogan on the relationship between unitary representations of
     reductive groups and Hermitian Harish-Chandra modules
+* Add some comments on how the concept of coherent families is useful to other
+  problems too
+
+* Make a proper discussion on basis
+* Make a proper discussion of highest weight modules