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authorKarl Berry <karl@freefriends.org>2018-07-24 21:40:01 +0000
committerKarl Berry <karl@freefriends.org>2018-07-24 21:40:01 +0000
commitdd5d760ec124ea275aa4aa08e6ed9e49a795b84e (patch)
treee7a5a4c76040e36ee5779ff2ad931d4b52053334 /Master/texmf-dist/doc/latex/dynkin-diagrams
parent4483084c8db90781ab093857710cdcaf72972327 (diff)
dynkin-diagrams (24jul18)
git-svn-id: svn://tug.org/texlive/trunk@48265 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/dynkin-diagrams')
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/README6
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib18
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdfbin604888 -> 615986 bytes
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex269
4 files changed, 155 insertions, 138 deletions
diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/README b/Master/texmf-dist/doc/latex/dynkin-diagrams/README
index 988e4282461..aec363034d8 100644
--- a/Master/texmf-dist/doc/latex/dynkin-diagrams/README
+++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/README
@@ -2,9 +2,9 @@ ___________________________________
Dynkin diagrams
- v3.13
+ v3.14
- 18 July 2018
+ 24 July 2018
___________________________________
Authors : Ben McKay
@@ -16,4 +16,4 @@ Licence : Released under the LaTeX Project Public License v1.3c or
----------------------------------------------------------------------
Draws Dynkin, Coxeter and Satake di­a­grams in LaTeX doc­u­ments, us­ing the TikZ pack­age.
-Version 3.13 allows colouring of arrows.
+Version 3.14 simplifies drawing braces under several nodes.
diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib
index c364aec770d..7c3d1e98f82 100644
--- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib
+++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib
@@ -2,6 +2,24 @@
% Encoding: ISO8859_1
+@Book{Adams:1996,
+ Title = {Lectures on exceptional {L}ie groups},
+ Author = {Adams, J. F.},
+ Publisher = {University of Chicago Press, Chicago, IL},
+ Year = {1996},
+ Note = {With a foreword by J. Peter May,
+ Edited by Zafer Mahmud and Mamoru Mimura},
+ Series = {Chicago Lectures in Mathematics},
+
+ ISBN = {0-226-00526-7; 0-226-00527-5},
+ Mrclass = {22-01 (22E10)},
+ Mrnumber = {1428422},
+ Mrreviewer = {William M. McGovern},
+ Owner = {user},
+ Pages = {xiv+122},
+ Timestamp = {2018.07.22}
+}
+
@Article{Baba:2009,
Title = {Satake diagrams and restricted root systems of semisimple pseudo-{R}iemannian symmetric spaces},
Author = {Baba, Kurando},
diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf
index c459a92e088..db65efc4e9f 100644
--- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf
+++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex
index 806a2960d67..b4978b6034b 100644
--- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex
+++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex
@@ -1,8 +1,8 @@
\documentclass{amsart}
-\title{The Dynkin diagrams package \\ Version 3.13}
+\title{The Dynkin diagrams package \\ Version 3.14}
\author{Ben McKay}
-\date{18 July 2018}
+\date{24 July 2018}
\usepackage{etex}
\usepackage[T1]{fontenc}
@@ -126,7 +126,10 @@ before upper={\widowpenalties=3 10000 10000 150}}
\fi}
\makeatother
+\fvset{fontsize=\small}
+
\begin{document}
+
\maketitle
\begin{center}
\begin{varwidth}{\textwidth}
@@ -303,6 +306,23 @@ We use a solid gray bar to denote the folding of a Dynkin diagram, rather than t
\end{tikzpicture}
\end{tcblisting}
+\begin{tcblisting}{title={Labelling several roots}}
+\begin{tikzpicture}
+\dynkin{A}{*.*x*.*}
+\dynkinBrace[p]{1}{2}
+\dynkinBrace[q]{4}{5}
+\end{tikzpicture}
+\end{tcblisting}
+
+\begin{tcblisting}{title={Labelling several roots, and a starred form}}
+\begin{tikzpicture}
+\dynkin{A}{10}
+\dynkinBrace[\text{Roots 2 to 9}]{2}{9}
+\dynkinBrace*[\text{Roots 3 to 8}]{3}{8}
+\end{tikzpicture}
+\end{tcblisting}
+
+
\section{Style}
\begin{tcblisting}{title={Colours}}
@@ -393,6 +413,10 @@ The mark list \verb!oo**ttxx! has one mark for each root: \verb!o!, \verb!o!, \d
Roots are listed in the current default ordering.
(Careful: in an affine root system, a mark list will \emph{not} contain a mark for root zero.)
+If you need to repeat a mark, you can give a \emph{single digit} positive integer to indicate how many times to repeat it.
+\begin{tcblisting}{title={A mark list with repetitions}}
+\dynkin{A}{x4o3t4}
+\end{tcblisting}
\NewDocumentCommand\ClassicalLieSuperalgebras{om}%
{%
@@ -563,6 +587,8 @@ D_4 &
\endgroup
+
+
\section{Parabolic subgroups}
Each set of roots is assigned a number, with each binary digit zero or one to say whether the corresponding root is crossed or not:
@@ -572,48 +598,31 @@ projective 3-space is associated to
the Dynkin diagram \dynkin[parabolic=3]{A}{3}.
\end{tcblisting}
-\NewDocumentCommand\HSS{mommm}%
-{%
- \begingroup
- \renewcommand*{\arraystretch}{1.2}
- \begin{tabular}{@{}>{$}r<{$}@{}m{6cm}@{}}
- \\
- \IfNoValueTF{#2}%
- {%
- #1 & \dynkin{#3}{#4} \\
- & \csDynkin{#3}{#4} \\
- }%
- {%
- #1 & \dynkin[#2]{#3}{#4} \\
- & \csDynkin[#2]{#3}{#4} \\
- }%
- & #5%
- \\[.75em]
- \end{tabular}
- \endgroup
- \\
-}%
-
-\renewcommand*{\arraystretch}{1}
-\begin{longtable}{>{\columncolor[gray]{.9}}p{7cm}}
-\caption{The Hermitian symmetric spaces}
-\endfirsthead
-\caption{\dots continued}\\
-\endhead
-\caption{continued \dots}\\
-\endfoot
+\begin{filecontents*}{hermitian-symmetric-spaces.tex}
+\NewDocumentCommand\HSS{mommm}
+{#1&\IfNoValueTF{#2}{\dynkin{#3}{#4}}{\dynkin[parabolic=#2]{#3}{#4}}&#5\\}
+\renewcommand*{\arraystretch}{1.5}
+\begin{longtable}
+{>{\columncolor[gray]{.9}}>$l<$>{\columncolor[gray]{.9}}>$l<$>{\columncolor[gray]{.9}}l}
+\caption{The Hermitian symmetric spaces}\endfirsthead
+\caption{\dots continued}\\ \endhead
+\caption{continued \dots}\\ \endfoot
\endlastfoot
\HSS{A_n}{A}{**.*x*.**}{Grassmannian of $k$-planes in $\C{n+1}$}
-\HSS{B_n}[parabolic=1]{B}{}{$(2n-1)$-dimensional hyperquadric, i.e. the variety of null lines in $\C{2n+1}$}
-\HSS{C_n}[parabolic=16]{C}{}{space of Lagrangian $n$-planes in $\C{2n}$}
-\HSS{D_n}[parabolic=1]{D}{}{$(2n-2)$-dimensional hyperquadric, i.e. the variety of null lines in $\C{2n}$}
-\HSS{D_n}[parabolic=32]{D}{}{one component of the variety of maximal dimension null subspaces of $\C{2n}$}
-\HSS{D_n}[parabolic=16]{D}{}{the other component}
-\HSS{E_6}[parabolic=1]{E}{6}{complexified octave projective plane}
-\HSS{E_6}[parabolic=32]{E}{6}{its dual plane}
-\HSS{E_7}[parabolic=64]{E}{7}{the space of null octave 3-planes in octave 6-space}
+\HSS{B_n}[1]{B}{}{$(2n-1)$-dimensional hyperquadric, i.e. the variety of null lines in $\C{2n+1}$}
+\HSS{C_n}[16]{C}{}{space of Lagrangian $n$-planes in $\C{2n}$}
+\HSS{D_n}[1]{D}{}{$(2n-2)$-dimensional hyperquadric, i.e. the variety of null lines in $\C{2n}$}
+\HSS{D_n}[32]{D}{}{one component of the variety of maximal dimension null subspaces of $\C{2n}$}
+\HSS{D_n}[16]{D}{}{the other component}
+\HSS{E_6}[1]{E}{6}{complexified octave projective plane}
+\HSS{E_6}[32]{E}{6}{its dual plane}
+\HSS{E_7}[64]{E}{7}{the space of null octave 3-planes in octave 6-space}
\end{longtable}
-
+\end{filecontents*}
+\begingroup
+\input{hermitian-symmetric-spaces.tex}
+\endgroup
+\VerbatimInput{hermitian-symmetric-spaces.tex}
@@ -645,6 +654,9 @@ The extended Dynkin diagrams are also described in the notation of Kac \cite{Kac
\end{dynkinTable}
+
+
+
\section{Affine twisted and untwisted Dynkin diagrams}
The affine Dynkin diagrams are described in the notation of Kac \cite{Kac:1990} p. 55:
@@ -717,11 +729,14 @@ D^{(3)}_4=\dynkin{D}[3]{4}\)
\end{dynkinTable}
+
+
+
\section{Kac style}
We include a style called \verb!Kac! which tries to imitate the style of \cite{Kac:1990}.
-\begin{tcblisting}{title={Kac style}}
+\begin{tcblisting}{title={Kac style},colback=white}
\dynkin[Kac]{F}{4}
\end{tcblisting}
@@ -746,6 +761,7 @@ We include a style called \verb!Kac! which tries to imitate the style of \cite{K
+
\section{Folded Dynkin diagrams}
The Dynkin diagrams package has limited support for folding Dynkin diagrams.
@@ -939,6 +955,11 @@ G_2 & \dynk{G}{2}
\end{dynkinTable}
\endgroup
+
+
+
+
+
\section{Root ordering}\label{section:order}
\begin{tcblisting}{title={Root ordering}}
@@ -949,21 +970,16 @@ G_2 & \dynk{G}{2}
\dynkin[label,ordering=Kac]{E}{6}
\end{tcblisting}
Default is Bourbaki.
+Sources are Adams \cite{Adams:1996} p. 56--57, Bourbaki \cite{Bourbaki:2002} p. pp. 265--290 plates I-IX, Carter \cite{Carter:2005} p. 540--609, Dynkin \cite{Dynkin:1952}, Kac \cite{Kac:1990} p. 43.
\NewDocumentCommand\tablerow{mm}%
{%
-#1_{#2}
-&
-\dynkin[label,ordering=Adams]{#1}{#2}
-&
-\dynkin[label]{#1}{#2}
-&
-\dynkin[label,ordering=Carter]{#1}{#2}
-&
-\dynkin[label,ordering=Dynkin]{#1}{#2}
-&
-\dynkin[label,ordering=Kac]{#1}{#2}
-\\
+#1_{#2}&
+\dynkin[label,ordering=Adams]{#1}{#2}&
+\dynkin[label]{#1}{#2}&
+\dynkin[label,ordering=Carter]{#1}{#2}&
+\dynkin[label,ordering=Dynkin]{#1}{#2}&
+\dynkin[label,ordering=Kac]{#1}{#2}\\
}%
\begin{center}
@@ -974,20 +990,38 @@ Default is Bourbaki.
& Adams & Bourbaki & Carter & Dynkin & Kac \\ \midrule
\endfirsthead
\toprule
-Adams & Bourbaki & Carter & Dynkin & Kac \\ \midrule
+& Adams & Bourbaki & Carter & Dynkin & Kac \\ \midrule
\endhead
\bottomrule
\endfoot
\bottomrule
\endlastfoot
-\tablerow{E}{6}
-\tablerow{E}{7}
-\tablerow{E}{8}
-\tablerow{F}{4}
-\tablerow{G}{2}
+\tablerow{E}{6}\tablerow{E}{7}\tablerow{E}{8}\tablerow{F}{4}\tablerow{G}{2}
\end{longtable}
\end{center}
+The marks are set down in order according to the current root ordering:
+\begin{tcblisting}{}
+\begin{tikzpicture}
+\dynkin[label]{E}{*otxXOt*}
+\end{tikzpicture}
+\end{tcblisting}
+
+\begin{tcblisting}{}
+\begin{tikzpicture}
+\dynkin[label,ordering=Carter]{E}{*otxXOt*}
+\end{tikzpicture}
+\end{tcblisting}
+
+\begin{tcblisting}{}
+\begin{tikzpicture}
+\dynkin[label,ordering=Kac]{E}{*otxXOt*}
+\end{tikzpicture}
+\end{tcblisting}
+
+
+
+
\section{Connecting Dynkin diagrams}\label{section:name}
@@ -1318,85 +1352,50 @@ Below we draw the Vogan diagrams of some affine Lie superalgebras \cite{Ransingh
\endgroup
-\begingroup
+\begin{filecontents*}{simple-lie-algebras.tex}
+\NewDocumentEnvironment{bunch}{}%
+{\renewcommand*{\arraystretch}{1}\begin{array}{@{}ll@{}}\\ \midrule}{\\ \midrule\end{array}}
\small
-\newcolumntype{F}{>{\columncolor[gray]{.9}}>{$}m{\wdtD}<{$}}
-\newcolumntype{G}{>{\columncolor[gray]{.9}}>{$}m{\wdtE}<{$}}
-\newcolumntype{H}{>{\columncolor[gray]{.9}}>{$}m{\wdtL}<{$}}
-\newcolumntype{I}{>{\columncolor[gray]{.9}}>{$}m{3cm}<{$}}
-\RenewDocumentCommand\wdtA{}{.2cm}
-\RenewDocumentCommand\wdtD{}{2.1cm}
-\RenewDocumentCommand\wdtE{}{4.1cm}
-\RenewDocumentCommand\wdtL{}{3.5cm}
-\NewDocumentCommand\LieG{}{\ensuremath{\mathfrak{g}}}
-\NewDocumentCommand\R{m}{\ensuremath{\mathbb{R}^{#1}}}
+\NewDocumentCommand\nct{mm}{\newcolumntype{#1}{>{\columncolor[gray]{.9}}>{$}m{#2cm}<{$}}}
+\nct{G}{.3}\nct{D}{2.1}\nct{W}{2.8}\nct{R}{3.7}\nct{S}{3}
+\NewDocumentCommand\LieG{}{\mathfrak{g}}
+\NewDocumentCommand\W{om}{\ensuremath{\mathbb{Z}^{#2}\IfValueT{#1}{/\left<#1\right>}}}
\renewcommand*{\arraystretch}{1.5}
-\begin{longtable}{ADIGH}
-\LieG & \text{diagram} & V & \Delta & \alpha_i \\ \midrule
-\endfirsthead
-\LieG & \text{diagram} & V & \Delta & \alpha_i \\ \midrule
-\endhead
-A_n & \dynkin{A}{} &
-\R{n+1}/\left<\sum e_j\right> & e_i-e_j & e_i-e_{i+1} \\
-B_n & \dynkin{B}{} &
-\R{n} & \pm e_i, \pm e_i \pm e_j, i\ne j & e_i-e_{i+1}, e_n \\
-C_n & \dynkin{C}{} &
-\R{n} & \pm 2 e_i, \pm e_i \pm e_j, i\ne j & e_i-e_{i+1}, 2e_n \\
-D_n & \dynkin{D}{} & \R{n} & \pm e_i \pm e_j, i\ne j & \begin{cases}e_i-e_{i+1}, & i\le n-2 \\ e_{n-1}+e_n \end{cases} \\
-E_8 & \dynkin{E}{8} & \R{8} &
-\begin{cases}
-\pm 2 e_i \pm 2 e_j, & i \ne j, \\
-\sum_i (-1)^{m_i} e_i, & \sum m_i \text{ even}
-\end{cases}
-&
-\begin{cases}
-2e_1-2e_2, \\
-2e_2-2e_3, \\
-2e_3-2e_4, \\
-2e_4-2e_5, \\
-2e_5-2e_6, \\
-2e_6+2e_7, \\
--\sum e_j, \\
-2e_6-2e_7
-\end{cases}
-\\
-E_7 & \dynkin{E}{7} &
-\R{8}/\left<e_1-e_2\right>
-& \text{quotient of } E_8 & \text{quotient of } E_8
-\\
-E_6 & \dynkin{E}{6} & \R{8}/\left<e_1-e_2,e_2-e_3\right> & \text{quotient of } E_8 & \text{quotient of } E_8
-\\
-F_4 & \dynkin{F}{4} & \R{4} &
-\begin{cases}
-\pm 2e_i, \\
-\pm 2e_i \pm 2e_j, i \ne j, \\
-\pm e_1 \pm e_2 \pm e_3 \pm e_4
-\end{cases}
-&
-\begin{cases}
-2e_2-2e_3, \\
-2e_3-2e_4, \\
-2e_4, \\
-e_1-e_2-e_3-e_4
-\end{cases}
-\\
-G_2 & \dynkin{G}{2} & \R{3}/\left<\sum e_j\right>
-& \begin{cases}
-\pm(1,-1,0), & \\
-\pm(-1,0,1), & \\
-\pm(0,-1,1), & \\
-\pm(2,-1,-1), & \\
-\pm(1,-2,1), & \\
-\pm(-1,-1,2)
-\end{cases}
-& \begin{cases}
-(-1,0,1), & \\
-(2,-1,-1)
-\end{cases}
+\NewDocumentCommand\quo{}{\text{quotient of } E_8}
+\begin{longtable}{@{}GDWRS@{}}
+\LieG&\text{Diagram}&\text{Weights}&\text{Roots}&\text{Simple roots}\\ \midrule\endfirsthead
+\LieG&\text{Diagram}&\text{Weights}&\text{Roots}&\text{Simple roots}\\ \midrule\endhead
+A_n&\dynkin{A}{}&\W[\sum e_j]{n+1}&e_i-e_j&e_i-e_{i+1}\\
+B_n&\dynkin{B}{}&\W{n}& \pm e_i, \pm e_i \pm e_j, i\ne j&e_i-e_{i+1}, e_n\\
+C_n&\dynkin{C}{}&\W{n}& \pm 2 e_i, \pm e_i \pm e_j, i\ne j&e_i-e_{i+1}, 2e_n\\
+D_n&\dynkin{D}{}&\W{n}& \pm e_i \pm e_j, i\ne j &
+\begin{bunch}e_i-e_{i+1},&i\le n-1\\e_{n-1}+e_n\end{bunch}\\
+E_8&\dynkin{E}{8}&\W{8}&
+\begin{bunch}\pm2e_i\pm2e_j,&i\ne j,\\ \sum_i(-1)^{m_i}e_i,&\sum m_i \text{ even}\end{bunch}&
+\begin{bunch}
+2e_1-2e_2,\\2e_2-2e_3,\\2e_3-2e_4,\\2e_4-2e_5,\\2e_5-2e_6,\\2e_6+2e_7,\\
+-\sum e_j,\\2e_6-2e_7
+\end{bunch}\\
+E_7&\dynkin{E}{7}&\W[e_1-e_2]{8}&\quo&\quo\\
+E_6&\dynkin{E}{6}&\W[e_1-e_2,e_2-e_3]{8}&\quo&\quo\\
+F_4& \dynkin{F}{4}&\W{4}&
+\begin{bunch}\pm 2e_i,\\ \pm 2e_i \pm 2e_j, \quad i \ne j,\\ \pm e_1 \pm e_2 \pm e_3 \pm e_4
+\end{bunch}&
+\begin{bunch}2e_2-2e_3,\\2e_3-2e_4,\\2e_4,\\e_1-e_2-e_3-e_4\end{bunch}\\
+G_2&\dynkin{G}{2}&\W[\sum e_j]{3}&
+\begin{bunch}
+\pm(1,-1,0),\\ \pm(-1,0,1),\\ \pm(0,-1,1),\\ \pm(2,-1,-1),\\ \pm(1,-2,1),\\ \pm(-1,-1,2)
+\end{bunch}&
+\begin{bunch}(-1,0,1),\\(2,-1,-1)\end{bunch}
\end{longtable}
+\end{filecontents*}
+\newpage
+\begingroup
+\input{simple-lie-algebras.tex}
\endgroup
-
-
+\newpage
+\VerbatimInput{simple-lie-algebras.tex}
+\newpage
\section{Syntax}