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

Commit
baf429759782b1a48134994e68176ef5ffd3fc2a
Parent
97ef29fceb37ecb194e96a3c6a362a79bf9f0bd9
Author
Pablo <pablo-escobar@riseup.net>
Date

Changed the notation for the height of a weight

Diffstat

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}