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
Log
Files
Refs
README
LICENSE

Commit: e7bf45af59b37e75e14bbe0923887613c5f9deaf
Parent: e4156ebd9234c44a44269d8af459075a532634eb
Author: Pablo <pablo-escobar@riseup.net>
Date: Fri, 25 Nov 2022 21:07:34 +0000

Automated the "47 pages left" thing from chapter 2

Diffstat

3 files changed, 12 insertions, 3 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	preamble.tex	6	6	0
Modified	sections/complete-reducibility.tex	7	4	3
Modified	sections/mathieu.tex	2	2	0

diff --git a/preamble.tex b/preamble.tex
@@ -16,6 +16,7 @@
 \usepackage{rank-2-roots}
 \usepackage{fancyhdr}
 \usepackage{titling}
+\usepackage{refcount}
 
 % Configure how link look
 \hypersetup{
@@ -194,3 +195,8 @@
     \draw[shorten <=0.2em, #1] (#2.west) -- (#3.east);
   \end{tikzpicture}
 }
+
+% Command for printing the number of pages between two labels
+\newcommand{\pagedifference}[2]{%
+  \number\numexpr\getpagerefnumber{#2}-\getpagerefnumber{#1}\relax}
+

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -1,14 +1,15 @@
 \chapter{Semisimplicity \& Complete Reducibility}
 
-% TODO: Automate the "47 pages" thing
+\label{start-47}
+
 Having hopefully established in the previous chapter that Lie algebras and
 their representations are indeed useful, we are now faced with the Herculean
 task of trying to understand them. We have seen that representations can be
 used to derive geometric information about groups, but the question remains:
 how to we go about classifying the representations of a given Lie algebra? This
 is a question that have sparked an entire field of research, and we cannot hope
-to provide a comprehensive answer the 47 pages we have left. Nevertheless, we
-can work on particular cases.
+to provide a comprehensive answer in the \pagedifference{start-47}{end-47}
+pages we have left. Nevertheless, we can work on particular cases.
 
 For instance, one can readily check that a representation \(V\) of the
 \(n\)-dimensional Abelian Lie algebra \(K^n\) is nothing more than a choice of

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -1453,3 +1453,5 @@ subject.
 
 Alas, our journey has come to an end. All its left is to wonder at the beauty
 of Lie algebras and their representations.
+
+\label{end-47}