- Commit
- fc393aa5229b8b79c6ddd6939f92b93dc7d87d39
- Parent
- 9e9211b9a4a50a8dd1a5d9a3e66eef78dc081ea5
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Added a TODO item
Also added a BibTeX entry for Humphrey's book on the category 𝓞
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
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 :