30th-siicusp

A short lecture of mine on my scientific initiation project for 30th SIICUSP

git clone: git://git.pablopie.xyz/30th-siicusp
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Commit: b799fcd90729370309bae5fdd866095baba09c61
Parent: ff8d0204002ca07b45dc078e5028864021d785dd
Author: Pablo <pablo-escobar@riseup.net>
Date: Mon, 17 Oct 2022 20:02:47 +0000

Minor tweaks in notation

Diffstat

1 file changed, 7 insertions, 3 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	main.tex	10	7	3

diff --git a/main.tex b/main.tex
@@ -219,8 +219,12 @@
     \item \(\mathfrak{h} \subset \mathfrak{g}\) \emph{subálgebra de Cartan}
       \begin{gather*}
         V = \bigoplus_{\lambda \in \mathfrak{h}^*} V_\lambda \\
-        V_\lambda 
-        = \{v \in V : H v = \lambda(H) \cdot v \; \forall H \in \mathfrak{h} \}
+        V_\lambda =
+        \{
+          v \in V :
+          H \cdot v = \lambda(H) \cdot v
+          \quad \forall H \in \mathfrak{h}
+        \}
       \end{gather*}
 
     \item \emph{Pesos}: ``autovalores'' da ação de \(\mathfrak{h}\)
@@ -231,7 +235,7 @@
     \item \(V\) é determinado por seu maior peso!
 
     \item Módulos de Verma \(M(\lambda) = \mathcal{U}(\mathfrak{g})
-      \otimes_{\mathcal{U}(\mathfrak{b})} \mathbb{C}_\lambda\)
+      \otimes_{\mathcal{U}(\mathfrak{b})} k v_\lambda^+\)
   \begin{center}
     \begin{tikzcd}
       \cdots \arrow[bend left=60]{r}{-10}