- Commit
- baf429759782b1a48134994e68176ef5ffd3fc2a
- Parent
- 97ef29fceb37ecb194e96a3c6a362a79bf9f0bd9
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Changed the notation for the height of a weight
Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules
Changed the notation for the height of a weight
1 file changed, 4 insertions, 3 deletions
Status | File Name | N° Changes | Insertions | Deletions |
Modified | sections/semisimple-algebras.tex | 7 | 4 | 3 |
diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex @@ -452,9 +452,10 @@ order in \(Q\), where elements are ordered by their \emph{heights}. \begin{definition} Let \(\Sigma = \{\beta_1, \ldots, \beta_k\}\) be a basis for \(\Delta\). Given \(\alpha = n_1 \beta_1 + \cdots + n_2 \beta_2 \in Q\) with \(n_1, - \ldots, n_k \in \mathbb{Z}\), we call the number \(h(\alpha) = n_1 + \cdots + - n_k \in \mathbb{Z}\) \emph{the height of \(\alpha\)}. We say that \(\alpha - \preceq \beta\) if \(h(\alpha) \le h(\beta)\). + \ldots, n_k \in \mathbb{Z}\), we call the number \(\operatorname{ht}(\alpha) + = n_1 + \cdots + n_k \in \mathbb{Z}\) \emph{the height of \(\alpha\)}. We say + that \(\alpha \preceq \beta\) if \(\operatorname{ht}(\alpha) \le + \operatorname{ht}(\beta)\). \end{definition} \begin{definition}