diff options
11 files changed, 269 insertions, 50 deletions
diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/DoneTwoElBendy.tex b/Master/texmf-dist/doc/latex/dynkin-diagrams/DoneTwoElBendy.tex new file mode 100644 index 00000000000..b878b676b8d --- /dev/null +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/DoneTwoElBendy.tex @@ -0,0 +1,5 @@ +\begin{dynkinDiagram}[ply=4]{D}[1]% +{****.*****.*****} + \dynkinFold[bend right=90]{1}{13} + \dynkinFold[bend right=90]{0}{14} +\end{dynkinDiagram} diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/DoneTwoElStraight.tex b/Master/texmf-dist/doc/latex/dynkin-diagrams/DoneTwoElStraight.tex new file mode 100644 index 00000000000..f74b7f7b198 --- /dev/null +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/DoneTwoElStraight.tex @@ -0,0 +1,6 @@ +\begin{dynkinDiagram}[ply=4]{D}[1]% +{****.*****.*****} + \dynkinFold{0}{1} + \dynkinFold{1}{13} + \dynkinFold{13}{14} +\end{dynkinDiagram} diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/EulerProducts.tex b/Master/texmf-dist/doc/latex/dynkin-diagrams/EulerProducts.tex new file mode 100644 index 00000000000..f087ce48b64 --- /dev/null +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/EulerProducts.tex @@ -0,0 +1,61 @@ +\tikzset{/Dynkin diagram,ordering=Dynkin,label macro/.code={\alpha_{#1}}} +\newcounter{EPNo} +\setcounter{EPNo}{0} +\NewDocumentCommand\EP{smmmm}% +{% +\stepcounter{EPNo}\roman{EPNo}. & +\def\eL{.6cm} +\IfStrEqCase{#2}% +{% +{D}{\gdef\eL{1cm}}% +{E}{\gdef\eL{.75cm}}% +{F}{\gdef\eL{.35cm}}% +{G}{\gdef\eL{.35cm}}% +}% +\tikzset{/Dynkin diagram,edge length=\eL} +\IfBooleanTF{#1}% +{\dynkin[backwards,labels*={#4},labels={#5}]{#2}{#3}} +{\dynkin[labels*={#4},labels={#5}]{#2}{#3}} +\\ +}% +\begin{longtable}{MM} +\caption{Dynkin diagrams from Euler products \cite{Langlands:1967}}\\ +\endfirsthead +\caption{\dots continued}\\ +\endhead +\multicolumn{2}{c}{continued \dots}\\ +\endfoot +\endlastfoot +\EP{A}{***.**}{1,1,1,1,1}{,1,2,n-1,n} +\EP{A}{***.**}{1,1,1,1,1}{1,2,n-1,n} +\EP{A}{**.***.*}{1,1,1,1,1,1}{1,2,m-1,,m,n} +\EP{B}{**.***}{2,2,2,2,1}{1,2,n-1,n} +\EP*{B}{***.**}{2,2,2,2,1}{n,n-1,2,1,} +\EP{C}{**.***}{1,1,1,1,2}{1,2,n-1,} +\EP*{C}{***.**}{1,1,1,1,2}{n,n-1,2,1,} +\EP{D}{**.****}{1,1,1,1,1,1}{1,2,n-2,n-1,n} +\EP{D}{**.****}{1,1,1,1,1,1}{1,2,n-2,n-1,n} +\EP{E}{6}{1,1,1,1,1,1}{1,...,5} +\EP*{E}{7}{1,1,1,1,1,1,1}{6,...,1} +\EP{E}{7}{1,1,1,1,1,1,1}{1,...,6} +\EP*{E}{8}{1,1,1,1,1,1,1,1}{7,...,1} +\EP{E}{8}{1,1,1,1,1,1,1,1}{1,...,7} +\EP{G}{2}{1,3}{,1} +\EP{G}{2}{1,3}{1} +\EP{B}{**.*.**}{2,2,2,2,1}{,1,2,n-1,n} +\EP{F}{4}{1,1,2,2}{,3,2,1} +\EP{C}{3}{1,1,2}{,2,1} +\EP{C}{**.***}{1,1,1,1,2}{,1,n-2,n-1,n} +\EP*{B}{3}{2,2,1}{1,2} +\EP{F}{4}{1,1,2,2}{1,2,3} +\EP{D}{**.****}{1,1,1,1,1,1}{1,2,n-2,n-2,n,n} +\EP{E}{6}{1,1,1,1,1,1}{1,2,3,4,,5} +\EP{E}{6}{1,1,1,1,1,1}{1,2,3,5,,4} +\EP*{E}{7}{1,1,1,1,1,1,1}{,5,...,1,6} +\EP*{E}{7}{1,1,1,1,1,1,1}{,6,4,3,2,1,5} +\EP*{E}{8}{1,1,1,1,1,1,1,1}{,6,...,1,7} +\EP*{E}{8}{1,1,1,1,1,1,1,1}{,7,5,4,3,2,1,6} +\EP*{E}{7}{1,1,1,1,1,1,1}{5,...,1,,6} +\EP*{E}{7}{1,1,1,1,1,1,1}{1,...,5,,6} +\EP*{E}{8}{1,1,1,1,1,1,1,1}{6,...,1,,7} +\end{longtable} diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/README b/Master/texmf-dist/doc/latex/dynkin-diagrams/README index cdd04fdf1f4..94427be9e29 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 - v3.141592 + v3.1415926 - 24 January 2019 + 25 November 2019 ___________________________________ Authors : Ben McKay @@ -16,6 +16,9 @@ Licence : Released under the LaTeX Project Public License v1.3c or ---------------------------------------------------------------------- Draws Dynkin diagrams in LaTeX documents, using the TikZ package. -Version 3.141592 fixes a rarely encountered problem with changing the default root marker and default affine root marker simultaneously, and smooths the ceref style indefinite edges. +Version 3.1415926 fixes problems with +(1) horizontal alignment of labels of varying heights, +(2) text styles being ignored. + diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/borovoi.tex b/Master/texmf-dist/doc/latex/dynkin-diagrams/borovoi.tex new file mode 100644 index 00000000000..f0664d22078 --- /dev/null +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/borovoi.tex @@ -0,0 +1,15 @@ +\tikzset{big arrow/.style={ + -Stealth,line cap=round,line width=1mm, + shorten <=1mm,shorten >=1mm}} +\newcommand\catholic[2]{\draw[big arrow,green!25!white] +(root #1) to (root #2);} +\newcommand\protestant[2]{ +\begin{scope}[transparency group, opacity=.25] +\draw[big arrow,orange] (root #1) to (root #2); +\end{scope}} +\begin{dynkinDiagram}[edge length=1.2cm, +indefinite edge/.style={thick,loosely dotted}, +labels*={0,1,2,3,\ell-3,\ell-2,\ell-1,\ell}]{D}[1]{} +\catholic{0}{6}\catholic{1}{7} +\protestant{7}{0}\protestant{6}{1} +\end{dynkinDiagram} diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/d44.tex b/Master/texmf-dist/doc/latex/dynkin-diagrams/d44.tex new file mode 100644 index 00000000000..482b805fa57 --- /dev/null +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/d44.tex @@ -0,0 +1,19 @@ +\tikzset{/Dynkin diagram,edge length=1cm,fold radius=1cm} +\tikzset{/Dynkin diagram,label macro/.code={\alpha_{#1}},label macro*/.code={\beta_{#1}}} +\({}^1 D_4\) 4-ply tied straight: +\begin{dynkinDiagram}[ply=4]{D}[1]% +{****.*****.*****} + \dynkinFold{0}{1} + \dynkinFold{1}{13} + \dynkinFold{13}{14} +\dynkinLabelRoots{0,...,14} +\dynkinLabelRoots*{0,...,14} +\end{dynkinDiagram} +\({}^1 D_4\) 4-ply tied bending: +\begin{dynkinDiagram}[ply=4]{D}[1]% +{****.*****.*****} + \dynkinFold{1}{13} + \dynkinFold[bend right=65]{0}{14} +\dynkinLabelRoots{0,...,14} +\dynkinLabelRoots*{0,...,14} +\end{dynkinDiagram} diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf Binary files differdeleted file mode 100644 index d28d05f96c2..00000000000 --- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdf +++ /dev/null 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 6d84d1606d9..b11488ffdd8 100644 --- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex @@ -1,6 +1,6 @@ \documentclass{amsart} -\title{The Dynkin diagrams package \\ Version 3.141592} +\title{The Dynkin diagrams package \\ Version 3.1415926} \makeatletter \DeclareRobustCommand{\scotsMc}{\scotsMcx{c}} @@ -20,16 +20,18 @@ \author{Ben \scotsMc{}Kay} \address{School of Mathematical Sciences, University College Cork, Cork, Ireland} \email{b.mckay@ucc.ie} -\date{24 January 2019} +\date{25 November 2019} \usepackage{etex} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenx} \usepackage{etoolbox} \usepackage{lmodern} +\RequirePackage[tt=lining]{cfr-lm} \usepackage[kerning=true,tracking=true]{microtype} \usepackage{amsmath} \usepackage{amsfonts} +\usepackage{mathtools} \usepackage{array} \usepackage{xstring} \usepackage{longtable} @@ -65,10 +67,10 @@ \newcommand{\C}[1]{\mathbb{C}^{#1}} \renewcommand*{\arraystretch}{1.5} -\NewDocumentCommand\wdtA{}{.7cm} -\NewDocumentCommand\wdtD{}{3cm} -\NewDocumentCommand\wdtE{}{6cm} -\NewDocumentCommand\wdtL{}{3cm} +\newcommand{\wdtA}{.7cm} +\newcommand{\wdtD}{3cm} +\newcommand{\wdtE}{6cm} +\newcommand{\wdtL}{3cm} \newcolumntype{A}{@{}>{\columncolor[gray]{.9}$}m{\wdtA}<{$}} \newcolumntype{B}{@{}>{\columncolor[gray]{.9}}m{\wdtA}} \newcolumntype{D}{>{\columncolor[gray]{.9}}m{\wdtD}} @@ -106,8 +108,8 @@ \NewDocumentEnvironment{dynkinTable}{mmm}% {% -\RenewDocumentCommand\wdtD{}{#2} -\RenewDocumentCommand\wdtL{}{#3} +\renewcommand{\wdtD}{#2} +\renewcommand{\wdtL}{#3} \begin{longtable}{ADM} \caption{#1}\\ \endfirsthead @@ -150,7 +152,6 @@ before upper={\widowpenalties=3 10000 10000 150}} \fvset{fontsize=\small} \begin{document} - \maketitle \begin{center} \begin{varwidth}{\textwidth} @@ -158,7 +159,6 @@ before upper={\widowpenalties=3 10000 10000 150}} \end{varwidth} \end{center} - \setlength{\arrayrulewidth}{1.5pt} \section{Quick introduction} @@ -185,7 +185,7 @@ The Dynkin diagram of \(B_3\) is \end{dynkinDiagram} \end{tcblisting} \begin{tcblisting}{title={Inside a \TikZ environment}} -The baseline controls the vertical alignment: +Baseline controls vertical alignment: the Dynkin diagram of \(B_3\) is \begin{tikzpicture}[baseline=(origin.base)] \dynkin{B}{3} @@ -208,6 +208,7 @@ the Dynkin diagram of \(B_3\) is \end{dynkinTable} + \section{Set options globally} \begin{tcolorbox}[title={Most options set globally \dots}] @@ -234,6 +235,7 @@ You can also pass options to the package in \verb!\usepackage!. + \section{Coxeter diagrams} \begin{tcblisting}{title={Coxeter diagram option}} @@ -259,6 +261,7 @@ You can also pass options to the package in \verb!\usepackage!. \dyn[Coxeter,gonality=n]{I}{} \end{dynkinTable} + \section{Satake diagrams}\label{section:Satake} \begin{tcblisting}{title={Satake diagrams use the standard name instead of a rank}} @@ -342,10 +345,10 @@ segment length=1mm,amplitude=.6mm}}} \section{Labels for the roots} \begin{tcblisting}{title={Make a macro to assign labels to roots}} -\dynkin[label,label macro/.code={\alpha_{#1}},edge length=.75cm]{D}{5} +\dynkin[label,label macro/.code={\alpha_{\mathrlap{#1}}},edge length=.75cm]{D}{5} \end{tcblisting} \begin{tcblisting}{title={Labelling several roots}} -\dynkin[labels={,2,...,5,,7},label macro/.code={\alpha_{#1}}]{A}{7} +\dynkin[labels={,2,...,5,,7},label macro/.code={\alpha_{\mathrlap#1}}]{A}{7} \end{tcblisting} \begin{tcblisting}{title={The \texttt{foreach} notation I}} \dynkin[labels={1,3,...,7},]{A}{9} @@ -354,7 +357,7 @@ segment length=1mm,amplitude=.6mm}}} \dynkin[labels={,\alpha_2,\alpha_...,\alpha_7},]{A}{7} \end{tcblisting} \begin{tcblisting}{title={The \texttt{foreach} notation III}} -\dynkin[label macro/.code={\beta_{#1}},labels={,2,...,7},]{A}{7} +\dynkin[label macro/.code={\beta_{\mathrlap{#1}}},labels={,2,...,7},]{A}{7} \end{tcblisting} \begin{tcblisting}{title={Label the roots individually by root number}} \dynkin[label]{B}{3} @@ -364,14 +367,9 @@ segment length=1mm,amplitude=.6mm}}} \dynkinLabelRoot{2}{\alpha_2} \end{dynkinDiagram} \end{tcblisting} -\begin{tcblisting}{title={Use a text style}} -\begin{dynkinDiagram}[text/.style={scale=1.2}]{B}{3}; -\dynkinLabelRoot{2}{\alpha_2} -\end{dynkinDiagram} -\end{tcblisting} \begin{tcblisting}{title={Access root labels via TikZ}} \begin{dynkinDiagram}{B}{3} -\node[below] at (root 2) {\(\alpha_2\)}; +\node[below] at (root 2) {\(\alpha_{\mathrlap{2}}\)}; \end{dynkinDiagram} \end{tcblisting} \begin{tcblisting}{title={Commands to label several roots}} @@ -387,8 +385,8 @@ segment length=1mm,amplitude=.6mm}}} \end{tcblisting} \begin{tcblisting}{title={Labelling several roots and alternates}} \dynkin[% -label macro/.code={\alpha_{#1}}, -label macro*/.code={\gamma_{#1}}, +label macro/.code={\alpha_{\mathrlap{#1}}}, +label macro*/.code={\gamma_{\mathrlap{#1}}}, labels={,2,...,5,,7}, labels*={1,3,4,5,6}]{A}{7} \end{tcblisting} @@ -399,6 +397,50 @@ labels*={1,3,4,5,6}]{A}{7} \end{dynkinDiagram} \end{tcblisting} +\section{Label subscripts} +Note the slight improvement that \verb!\mathrlap! makes: the labels are centered on the middle of the letter \(\alpha\), ignoring the space taken up by the subscripts. +\begin{tcblisting}{title={Label spacing improvement}} +\dynkin[label,label macro/.code={\alpha_{#1}},edge length=.75cm]{D}{15} +\par\noindent{}% +\dynkin[label,label macro/.code={\alpha_{\mathrlap{#1}}},edge length=.75cm]{D}{15} +\end{tcblisting} + + +\section{Height and depth of labels} +Labels are set with default maximum height the height of the character \(b\), and default maximum depth the depth of the character \(g\). +To change these, set \verb!label height! and \verb!label depth!: +\begin{tcblisting}{title={Change height and dept of characters}} +\dynkin[labels={a,b,c,d}]{F}{4} +\dynkin[labels*={a,b,c,d}]{F}{4} +\dynkin[% +label macro/.code={\alpha_{\mathrlap{#1}}}, +label macro*/.code={\gamma_{\mathrlap{#1}}}, +label height=$\alpha_1$, +label depth=$\alpha_1$, +labels={,2,...,5,,7}, +labels*={1,3,4,5,6}]{A}{7} +\dynkin[labels={A,B,C,D},label height=$A$,label depth=$A$]{F}{4} +\dynkin[labels={a^1,b^2,c^3,d^4},label height=$X^X$]{F}{4} +\end{tcblisting} + +\section{Text style for the labels} +\begin{tcblisting}{title={Use a text style: big and blue}} +\begin{dynkinDiagram}[text style={scale=1.2,blue}, +edge length=.75cm, +labels={1,2,n-1,n}, +label macro/.code={\alpha_{\mathrlap{#1}}} +]{A}{} +\end{dynkinDiagram} +\end{tcblisting} +\begin{tcblisting}{title={Use a text style; font selection is in the label macro}} +\begin{dynkinDiagram}[text style={scale=1.2,blue}, +edge length=.75cm, +labels={1,2,n-1,n}, +label macro/.code={\mathbb{A}_{\mathrlap{#1}}}]{A}{} +\end{dynkinDiagram} +\end{tcblisting} + + \section{Bracing roots} \begin{tcblisting}{title={Bracing roots}} @@ -610,7 +652,7 @@ If you need to repeat a mark, you can give a \emph{single digit} positive intege \NewDocumentCommand\ClassicalLieSuperalgebras{om}% {% \IfValueT{#1}{\tikzset{/Dynkin diagram,root radius=#1}} -\RenewDocumentCommand\wdtE{}{10cm} +\renewcommand{\wdtE}{10cm} \begin{dynkinTable}{Classical Lie superalgebras \cite{Frappat/Sciarrino/Sorba:1989}. #2}{3.5cm}{6.5cm} \IfValueT{#1}{ & & \texttt{\textbackslash{}tikzset\{/Dynkin diagram,root radius=#1\}} \\ @@ -667,8 +709,8 @@ For such rare situations, there is an option: \begingroup -\RenewDocumentCommand\wdtA{}{.35cm} -\RenewDocumentCommand\wdtE{}{6.55cm} +\renewcommand{\wdtA}{.35cm} +\renewcommand{\wdtE}{6.55cm} \begin{dynkinTable}{Springer's table of indices \cite{Springer:2009}, pp. 320-321, with one form of \(E_7\) corrected}{2.5cm}{3.7cm} % 1 A_n & @@ -961,7 +1003,7 @@ We include a style called \verb!Kac! which tries to imitate the style of \cite{K \endgroup \section{Ceref style} -We include a style called \verb!ceref! which shapes the root markers more oblongly and with shadows. +We include a style called \verb!ceref! which paints oblong root markers with shadows. The word ``ceref'' is an old form of the word ``serif''. \begin{tcblisting}{title={Ceref style}} \dynkin[ceref]{F}{4} @@ -1045,9 +1087,9 @@ We have to be careful about the 4-ply foldings of \(D^{(1)}_{2\ell}\), for which \end{dynkinDiagram} \end{tcblisting} \begingroup -\RenewDocumentCommand\wdtA{}{.7cm} -\RenewDocumentCommand\wdtD{}{3.5cm} -\RenewDocumentCommand\wdtL{}{7cm} +\renewcommand{\wdtA}{.7cm} +\renewcommand{\wdtD}{3.5cm} +\renewcommand{\wdtL}{7cm} \NewDocumentCommand\seriesName{mmm}% {% \IfStrEq{#2}{0}{#1_{#3}}{#1^{#2}_{#3}}% @@ -1152,7 +1194,7 @@ We have to be careful about the 4-ply foldings of \(D^{(1)}_{2\ell}\), for which \end{longtable} \endgroup \begingroup -\RenewDocumentCommand\wdtA{}{.8cm} +\renewcommand{\wdtA}{.8cm} \begin{dynkinTable}{Frobenius fixed point subgroups of finite simple groups of Lie type \cite{Carter:1995} p. 15}{3cm}{6cm} A_{\ell\ge 1} & \dynk{A}{} {}^2\!A_{\ell\ge 2} & \dynk[fold]{A}{} @@ -1193,8 +1235,8 @@ Sources are Adams \cite{Adams:1996} p. 56--57, Bourbaki \cite{Bourbaki:2002} p. \dynkin[label,ordering=Kac]{#1}{#2}\\ }% \begin{center} -\RenewDocumentCommand\wdtA{}{.7cm} -\RenewDocumentCommand\wdtL{}{2.2cm} +\renewcommand{\wdtA}{.7cm} +\renewcommand{\wdtL}{2.2cm} \begin{longtable}{@{}ALLLLL@{}} \toprule & Adams & Bourbaki & Carter & Dynkin & Kac \\ \midrule @@ -1328,7 +1370,7 @@ Below we draw the Vogan diagrams of some affine Lie superalgebras \cite{Ransingh \begingroup \tikzset{/Dynkin diagram,label macro/.code=\labls{#1},label,root radius=.06cm} \tcbset{text width=10cm} -\RenewDocumentCommand\wdtA{}{2cm} +\renewcommand{\wdtA}{2cm} \NewDocumentEnvironment{Category}{m}% {% \begin{tcolorbox}[title={\(#1\)},breakable]{} @@ -1673,7 +1715,7 @@ The environment syntax is \verb!\begin{dynkinDiagram}! followed by the same para is computed as \(n=\sum 2^{i-1} a_i\), \(a_i=0\) or \(1\), to say that root \(i\) is crossed, i.e. a noncompact root. \\ \optionLabel{root radius}{\typ{number}cm}{.05cm} & size of the dots and of the crosses in the Dynkin diagram \\ -\optionLabel{text/.style}{\typ{TikZ style data}}{scale=.7} +\optionLabel{text style}{\typ{TikZ style data}}{scale=.7} & Style for any labels on the roots. \\ \optionLabel{mark}{\typ{o,O,t,x,X,*}}{*} & default root mark \\ @@ -1685,6 +1727,10 @@ is computed as \(n=\sum 2^{i-1} a_i\), \(a_i=0\) or \(1\), to say that root \(i\ & the current labelling scheme for roots. \\ \optionLabel{label macro*}{\typ{1-parameter \TeX{} macro}}{\texttt{\#1}} & the current labelling scheme for alternate roots. \\ +\optionLabel{label height}{\typ{1-parameter \TeX{} macro}}{b} +& the current maximal height of text labels for the roots, set by giving mathematics text of that height. \\ +\optionLabel{label depth}{\typ{1-parameter \TeX{} macro}}{g} +& the current maximal depth of text labels for the roots, set by giving mathematics text of that depth. \\ \optionLabel{make indefinite edge}{\typ{edge pair \(i\)-\(j\) or list of such}}{\{\}} & edge pair or list of edge pairs to treat as having indefinitely many roots on them. \\ \optionLabel{indefinite edge ratio}{\typ{float}}{1.6} diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/hermitian-symmetric-spaces.tex b/Master/texmf-dist/doc/latex/dynkin-diagrams/hermitian-symmetric-spaces.tex new file mode 100644 index 00000000000..4f688c7935f --- /dev/null +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/hermitian-symmetric-spaces.tex @@ -0,0 +1,19 @@ +\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}[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} diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/simple-lie-algebras.tex b/Master/texmf-dist/doc/latex/dynkin-diagrams/simple-lie-algebras.tex new file mode 100644 index 00000000000..f1dce2e3c30 --- /dev/null +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/simple-lie-algebras.tex @@ -0,0 +1,35 @@ +\NewDocumentEnvironment{bunch}{}% +{\renewcommand*{\arraystretch}{1}\begin{array}{@{}ll@{}}\\ \midrule}{\\ \midrule\end{array}} +\small +\NewDocumentCommand\nct{mm}{\newcolumntype{#1}{>{\columncolor[gray]{.9}}>{$}m{#2cm}<{$}}} +\nct{G}{.3}\nct{D}{2.1}\nct{W}{3}\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} +\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}{}&\frac{1}{r+1}\W[\sum e_j]{n+1}&e_i-e_j&e_i-e_{i+1}\\ +B_n&\dynkin{B}{}&\frac{1}{2}\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}{}&\frac{1}{2}\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}&\frac{1}{2}\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}&\frac{1}{2}\W[e_1-e_2]{8}&\quo&\quo\\ +E_6&\dynkin{E}{6}&\frac{1}{3}\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} 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 32e6c17833b..e644e6251ec 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 3.141592 +% Version 3.1415926 % % % This package draws Dynkin diagrams in LaTeX documents, using the TikZ package. @@ -18,7 +18,7 @@ % % \NeedsTeXFormat{LaTeX2e}[1994/06/01] -\ProvidesPackage{dynkin-diagrams}[2019/01/24 Dynkin diagrams] +\ProvidesPackage{dynkin-diagrams}[2019/11/25 Dynkin diagrams] \RequirePackage{tikz} \RequirePackage{xstring} \RequirePackage{xparse} @@ -39,7 +39,6 @@ fit, patterns, shadows} - %%% %%% Application programming interface: %%% See dynkin-diagrams.tex file for examples of use. @@ -862,15 +861,11 @@ decoration= arc (180:90:{\dynkin@fold@radius});% \ifdynkin@arrows% \ifdynkin@reverse@arrows% - \path[/Dynkin diagram,edge, - -{Computer Modern Rightarrow[\dynkin@arrow@color]}, - ,tips] + \path[-{Computer Modern Rightarrow[\dynkin@arrow@color]},tips] ($(\dynkin@root@name \the\@toRoot)$)% - arc (135:180:{\dynkin@fold@radius});% + arc (90:135:{\dynkin@fold@radius});% \else% - \path[/Dynkin diagram,edge, - -{Computer Modern Rightarrow[\dynkin@arrow@color]}, - ,tips] + \path[-{Computer Modern Rightarrow[\dynkin@arrow@color]},tips] ($(\dynkin@root@name \the\@fromRoot)$)% arc (180:135:{\dynkin@fold@radius});% \fi% @@ -1159,7 +1154,13 @@ decoration= \@toRoot=#4% }% \begin{scope}[on background layer]% - \draw[/Dynkin diagram,edge,double,double distance=\dynkin@root@radius,fill=none,#2]% + \draw[/Dynkin diagram, + edge, + double, + double distance=\dynkin@root@radius, + fill=none, + {Straight Barb[length=1pt]}-{Straight Barb[length=1pt]}, + #2]% ($(\dynkin@root@name \the\@fromRoot)$)% arc (90:-90:{\dynkin@fold@radius});% \draw[/Dynkin diagram,edge,fill=none,#2]% @@ -1712,7 +1713,7 @@ decoration= reverse arrows/.is if = dynkin@reverse@arrows, reverse arrows = false, reverse-arrows/.forward to = /Dynkin diagram/reverse arrows, - fold style/.style = {solid,draw=black!40,fill=none,line width=\dynkin@root@radius}, + fold style/.style = {solid,draw=black!40,fill=none,line width=\dynkin@root@radius,{Triangle Cap[]}-{Triangle Cap[]}}, fold-style/.forward to=/Dynkin diagram/fold style/.style, fold left style/.style = {}, fold-left-style/.forward to=/Dynkin diagram/fold left style/.style, @@ -1817,7 +1818,6 @@ decoration= Coxeter=false, ordering/.store in = \dynkin@ordering, ordering = Bourbaki, - text style/.style={scale=.7}, text-style/.forward to=/Dynkin diagram/text style/.style, label macro/.code = {\regurgitate{#1}}, label-macro/.forward to=/Dynkin diagram/label macro, @@ -1887,9 +1887,19 @@ decoration= fill=white, }, }, + label height/.style={/tikz/every label/.append style={text height={height("#1"}}}, + label depth/.style={/tikz/every label/.append style={text depth={depth("#1"}}}, + text style/.style={/tikz/every label/.append style={#1}}, default/.style = { + text style={scale=.7}, label/.is if = dynkin@label@the@roots, label = false, + label height/.default=b, + label depth/.default=g, + label height, + label depth, + label-height/.forward to = /Dynkin diagram/label height, + label-depth/.forward to = /Dynkin diagram/label depth, labels = {}, labels* = {}, at/.estore in = \dynkin@current@location, |