From dd5d760ec124ea275aa4aa08e6ed9e49a795b84e Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Tue, 24 Jul 2018 21:40:01 +0000 Subject: dynkin-diagrams (24jul18) git-svn-id: svn://tug.org/texlive/trunk@48265 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/doc/latex/dynkin-diagrams/README | 6 +- .../doc/latex/dynkin-diagrams/dynkin-diagrams.bib | 18 ++ .../doc/latex/dynkin-diagrams/dynkin-diagrams.pdf | Bin 604888 -> 615986 bytes .../doc/latex/dynkin-diagrams/dynkin-diagrams.tex | 269 ++++++++++----------- .../tex/latex/dynkin-diagrams/dynkin-diagrams.sty | 38 ++- 5 files changed, 184 insertions(+), 147 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 Binary files a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf and b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf 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}}\\} +\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 -& \text{quotient of } E_8 & \text{quotient of } E_8 -\\ -E_6 & \dynkin{E}{6} & \R{8}/\left & \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} diff --git a/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty b/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty index f62565b93e8..870e2c5842f 100644 --- a/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty +++ b/Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty @@ -2,7 +2,7 @@ % % The Dynkin Diagrams package. % -% Version 3.13 +% Version 3.14 % % % This package draws Dynkin diagrams in LaTeX documents, using the TikZ package. @@ -18,7 +18,7 @@ % % \NeedsTeXFormat{LaTeX2e}[1994/06/01] -\ProvidesPackage{dynkin-diagrams}[2018/07/18 Dynkin diagrams] +\ProvidesPackage{dynkin-diagrams}[2018/07/24 Dynkin diagrams] \RequirePackage{tikz} \RequirePackage{xstring} \RequirePackage{xparse} @@ -26,11 +26,7 @@ \RequirePackage{expl3} \RequirePackage{pgfkeys} \RequirePackage{pgfopts} -\usetikzlibrary{arrows,arrows.meta} -\usetikzlibrary{backgrounds} -\usetikzlibrary{calc} -\usetikzlibrary{decorations.markings} -\usetikzlibrary{fit} +\usetikzlibrary{arrows,arrows.meta,backgrounds,calc,decorations.markings,fit,patterns,snakes} %% %% Application programming interface: @@ -186,6 +182,30 @@ }% }% + +\NewDocumentCommand\dynkinBrace{somm}%[text]{start}{end} +{% +\draw[decoration= + { + brace, + \IfBooleanF{#1}{mirror}, + raise=0.05cm, + }, + decorate] + ($(root #3)-({\dynkin@root@radius},\IfBooleanTF{#1}{{-\dynkin@root@radius}}{{\dynkin@root@radius}})$) + -- + ($(root #4)+({\dynkin@root@radius},\IfBooleanTF{#1}{{\dynkin@root@radius}}{{-\dynkin@root@radius}})$) + node + [ + pos=0.5, + anchor=\IfBooleanTF{#1}{south}{north}, + yshift=\IfBooleanTF{#1}{1mm}{-1mm}, + /Dynkin diagram/text +] +{\IfValueT{#2}{\(#2\)}};% +} + + %% \dynkinPrintLabels %% Prints the default labels on the Dynkin diagram, in the given ordering. \newcommand{\dynkinPrintLabels}% @@ -1838,7 +1858,7 @@ \xdef\dynkin@twisted@series{#3}% \xdef\dynkin@user@string{#4}% \global\dynkin@ply=\dynkin@ply@value\relax% - \xdef\dynkin@indefinite@edge@length{(\dynkin@edge@length*\dynkin@indefinite@edge@ratio)}\relax% +\xdef\dynkin@indefinite@edge@length{(\dynkin@edge@length*\dynkin@indefinite@edge@ratio)}\relax% \xdef\dynkin@series{#2}% \IfStrEq{\dynkin@diagram@name}{anonymous}% {% @@ -2646,7 +2666,7 @@ \foreach \b in {1,...,\the\dynkin@nodes}% {% \StrChar{\dynkin@roots}{\b}[\c]% - \dynkinRootMark*{\c}{\b}% + \dynkinRootMark{\c}{\b}% }% \ifdynkin@is@extended% \dynkinRootMark*{\dynkin@affine@root@mark}{0}% -- cgit v1.2.3