- Commit
- 20117e2e20c0f2eb66b41e4a837fcf5e33ce02ba
- Parent
- 6b75623635f9613c22bb72584f71e7a877e71474
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Fixed a small typo
Fixed a typo regarding the order relation on Q
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
1 file changed, 1 insertion, 2 deletions
| Status | File Name | N° Changes | Insertions | Deletions |
| Modified | sections/fin-dim-simple.tex | 3 | 1 | 2 |
diff --git a/sections/fin-dim-simple.tex b/sections/fin-dim-simple.tex @@ -520,8 +520,7 @@ induces an order in \(Q\), where elements are ordered by their \emph{parabolic} if \(\mathfrak{p} \supset \mathfrak{b}\). \end{definition} -% TODO: This is a total order on Q, not a partial order -It should be obvious that the binary relation \(\preceq\) in \(Q\) is a partial +It should be obvious that the binary relation \(\preceq\) in \(Q\) is a total order. In addition, we may compare the elements of a given \(Q\)-coset \(\lambda + Q\) by comparing their difference with \(0 \in Q\). In other words, given \(\lambda \in \mu + Q\), we say \(\lambda \preceq \mu\) if \(\lambda -