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

git clone: git://git.pablopie.xyz/lie-algebras-and-their-representations
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Commit: 0025360cc4e2f69e42d7dff29ff4901c263f0eb7
Parent: 3ec5b4c1aba8b5f771c8ae7228050252b2f4796b
Author: Pablo <pablo-escobar@riseup.net>
Date: Fri, 12 May 2023 00:53:39 +0000

Removed manual page breaks

This manual page breaks were set before implementing boxed theorem environments and do not make sence anymore

Diffstat

2 files changed, 0 insertions, 8 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/complete-reducibility.tex	2	0	2
Modified	sections/sl2-sl3.tex	6	0	6

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -580,8 +580,6 @@ This implies\dots
   \end{center}
 \end{corollary}
 
-\newpage
-
 \begin{proof}
   We have an isomorphism of sequences
   \begin{center}

diff --git a/sections/sl2-sl3.tex b/sections/sl2-sl3.tex
@@ -422,8 +422,6 @@ so that \(X\) carries \(m\) to \(M_{\lambda + \alpha}\). In other words,
 \(\mathfrak{sl}_3(k)_\alpha\) \emph{acts on \(M\) by translating vectors
 between eigenspaces}.
 
-\newpage
-
 For instance \(\mathfrak{sl}_3(K)_{\alpha_1 - \alpha_3}\) will act on the
 adjoint \(\mathfrak{sl}_3(K)\)-modules via
 \begin{figure}[h]
@@ -525,8 +523,6 @@ eigenspace of the action of \(h\) on \(\bigoplus_{k \in \mathbb{Z}} M_{\lambda
 - k (\alpha_1 - \alpha_2)}\) associated with the eigenvalue \(\lambda(H) - 2k\)
 is precisely the weight space \(M_{\lambda - k (\alpha_2 - \alpha_1)}\).
 
-\newpage
-
 Visually,
 \begin{center}
   \begin{tikzpicture}
@@ -733,8 +729,6 @@ along this direction.
   0\) and \(f\) is irrational with respect to the lattice \(Q\).
 \end{definition}
 
-\newpage
-
 The next observation we make is that all others weights of \(M\) must lie in a
 sort of \(\frac{1}{3}\)-cone with apex at \(\lambda\), as shown in
 \begin{center}