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: fc393aa5229b8b79c6ddd6939f92b93dc7d87d39
Parent: 9e9211b9a4a50a8dd1a5d9a3e66eef78dc081ea5
Author: Pablo <pablo-escobar@riseup.net>
Date: Mon, 3 Jul 2023 20:02:34 +0000

Added a TODO item

Also added a BibTeX entry for Humphrey's book on the category 𝓞

Diffstat

2 files changed, 10 insertions, 0 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	references.bib	9	9	0
Modified	sections/coherent-families.tex	1	1	0

diff --git a/references.bib b/references.bib
@@ -45,6 +45,15 @@
   edition =   {1},
 }
 
+@book{humphreys-cat-o,
+  title =     {Representations of Semisimple Lie Algebras in the BGG Category $\mathcal{O}$},
+  author =    {E. Humphreys, James},
+  publisher = {American Mathematical Society},
+  year =      {2008},
+  series =    {Graduate Studies in Mathematics},
+  volume =    94,
+}
+
 @inproceedings{cohomologies-lie,
   booktitle = {Lie Groups and Lie Algebras II},
   title =     {Cohomologies of Lie Groups and Lie Algebras},

diff --git a/sections/coherent-families.tex b/sections/coherent-families.tex
@@ -148,6 +148,7 @@ combinatorial counterpart.
 \end{enumerate}
 
 % TODO: Explain beforehand why central characters exist and are unique
+% TODO: Cite the discussion on central characters of [humphreys-cat-o] here
 \begin{definition}
   Given a highest weight \(\mathfrak{g}\)-module \(M\) of highest weight
   \(\lambda\), the unique algebra homomorphism \(\chi_\lambda :