From f0145b0157ebca6d2b1a9815e2547e82c968dac4 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Sat, 5 May 2018 21:13:24 +0000 Subject: dynkin-diagrams (5may18) git-svn-id: svn://tug.org/texlive/trunk@47620 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/doc/latex/dynkin-diagrams/README | 6 +- .../doc/latex/dynkin-diagrams/dynkin-diagrams.bib | 61 ++++-- .../doc/latex/dynkin-diagrams/dynkin-diagrams.pdf | Bin 516997 -> 593579 bytes .../doc/latex/dynkin-diagrams/dynkin-diagrams.tex | 228 +++++++++++++++++++-- 4 files changed, 264 insertions(+), 31 deletions(-) (limited to 'Master/texmf-dist/doc/latex') diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/README b/Master/texmf-dist/doc/latex/dynkin-diagrams/README index 0ff5a44b400..4ccb2aec8db 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 - v3.11 + v3.12 - 28 February 2018 + 30 April 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 3.11 ensures the inclusion of the TikZ background library. \ No newline at end of file +Version 3.12 fixes an error in the EIV diagram, and adds some more examples. 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 30fc8b08f5c..8d3a8632fbe 100644 --- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib +++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib @@ -1,4 +1,4 @@ -% This file was created with JabRef 2.10b2. +% This file was created with JabRef 2.10. % Encoding: ISO8859_1 @@ -75,20 +75,23 @@ Url = {https://doi.org/10.1007/s00209-012-1030-z} } -@Article{Dynkin:1952, - Title = {Semisimple subalgebras of semisimple {L}ie algebras}, - Author = {Dynkin, E. B.}, - Journal = {Mat. Sbornik N.S.}, - Year = {1952}, - Note = {Reprinted in English translation in \cite{Dynkin:2000}.}, - Pages = {349--462 (3 plates)}, - Volume = {30(72)}, +@InCollection{Draper/Guido:2016, + Title = {On the real forms of the exceptional {L}ie algebra {$\mathfrak + e_6$} and their {S}atake diagrams}, + Author = {Draper Fontanals, Cristina and Guido, Valerio}, + Booktitle = {Non-associative and non-commutative algebra and operator + theory}, + Publisher = {Springer, Cham}, + Year = {2016}, + Pages = {211--226}, + Series = {Springer Proc. Math. Stat.}, + Volume = {160}, - Mrclass = {09.1X}, - Mrnumber = {0047629}, - Mrreviewer = {I. Kaplansky}, + Mrclass = {17B20 (17A75 17B25 17B60)}, + Mrnumber = {3613831}, + Mrreviewer = {Alberto Elduque}, Owner = {user}, - Timestamp = {2017.11.15} + Timestamp = {2018.04.30} } @Book{Dynkin:2000, @@ -107,6 +110,22 @@ Timestamp = {2017.11.15} } +@Article{Dynkin:1952, + Title = {Semisimple subalgebras of semisimple {L}ie algebras}, + Author = {Dynkin, E. B.}, + Journal = {Mat. Sbornik N.S.}, + Year = {1952}, + Note = {Reprinted in English translation in \cite{Dynkin:2000}.}, + Pages = {349--462 (3 plates)}, + Volume = {30(72)}, + + Mrclass = {09.1X}, + Mrnumber = {0047629}, + Mrreviewer = {I. Kaplansky}, + Owner = {user}, + Timestamp = {2017.11.15} +} + @Article{Frappat/Sciarrino/Sorba:1989, Title = {Structure of basic {L}ie superalgebras and of their affine extensions}, Author = {Frappat, L. and Sciarrino, A. and Sorba, P.}, @@ -322,6 +341,22 @@ Timestamp = {2017.11.15} } +@Book{Springer:2009, + Title = {Linear algebraic groups}, + Author = {Springer, T. A.}, + Publisher = {Birkh\"auser Boston, Inc., Boston, MA}, + Year = {2009}, + Edition = {second}, + Series = {Modern Birkh\"auser Classics}, + + ISBN = {978-0-8176-4839-8}, + Mrclass = {20G15 (14L10)}, + Mrnumber = {2458469}, + Owner = {user}, + Pages = {xvi+334}, + Timestamp = {2018.03.31} +} + @InCollection{Zuber:1998, Title = {Generalized {D}ynkin diagrams and root systems and their folding}, Author = {Zuber, Jean-Bernard}, 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 94325f2c1f2..c5cc4b5147a 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 97a121f1439..5557830a45c 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 3.11} +\title{The Dynkin diagrams package \\ Version 3.12} \author{Ben McKay} -\date{28 February 2018} +\date{30 April 2018} \usepackage{etex} \usepackage[T1]{fontenc} @@ -33,7 +33,6 @@ \usepackage{xspace} \newcommand{\TikZ}{Ti\textit{k}Z\xspace} \usepackage{filecontents} -\usetikzlibrary{backgrounds} \usetikzlibrary{decorations.markings} \arrayrulecolor{white} \makeatletter @@ -49,9 +48,11 @@ \renewcommand*{\arraystretch}{1.5} \NewDocumentCommand\wdtA{}{.7cm} \NewDocumentCommand\wdtD{}{3cm} +\NewDocumentCommand\wdtE{}{6cm} \NewDocumentCommand\wdtL{}{3cm} \newcolumntype{A}{@{}>{\columncolor[gray]{.9}$}m{\wdtA}<{$}} \newcolumntype{D}{>{\columncolor[gray]{.9}}m{\wdtD}} +\newcolumntype{E}{>{\columncolor[gray]{.9}}m{\wdtE}} \newcolumntype{L}{>{\columncolor[gray]{.9}}p{\wdtL}} \newcolumntype{P}{>{\columncolor[gray]{.9}}p{10cm}} \NewDocumentCommand\textleftcurly{}{\texttt{\char'173}}% @@ -78,9 +79,10 @@ \NewDocumentCommand\dyn{omom}% {% - {#2}_{\typesetSubseries{#4}}^{\IfInteger{#3}{#3}{}} & \dynk[#1]{#2}[#3]{#4}% + {#2}_{\typesetSubseries{#4}}^{\IfInteger{#3}{#3}{\IfStrEq{#1}{extended}{1}{}}} & \dynk[#1]{#2}[#3]{#4}% }% + \NewDocumentEnvironment{dynkinTable}{mmm}% {% \RenewDocumentCommand\wdtD{}{#2} @@ -101,7 +103,7 @@ \definecolor{example-color}{gray}{1} -\definecolor{example-border-color}{gray}{.7} +\definecolor{example-border-color}{gray}{.7} \tcbset{coltitle=black,colback=example-color,colframe=example-border-color,enhanced,breakable,pad at break*=1mm, toprule=1.2mm,bottomrule=1.2mm,leftrule=1mm,rightrule=1mm,toprule at break=-1mm,bottomrule at break=-1mm, @@ -127,6 +129,11 @@ before upper={\widowpenalties=3 10000 10000 150}} \begin{document} + + + + + \maketitle \begin{center} \begin{varwidth}{\textwidth} @@ -138,23 +145,26 @@ before upper={\widowpenalties=3 10000 10000 150}} \setlength{\arrayrulewidth}{1.5pt} - \section{Quick introduction} - - \begin{tcolorbox}[title={Load the Dynkin diagram package (see options below)}] \begin{verbatim} +\documentclass{amsart} \usepackage{dynkin-diagrams} +\begin{document} +The Dynkin diagram of \(B_3\) is \dynkin{B}{3}. +\end{document} \end{verbatim} \end{tcolorbox} \begin{tcblisting}{title={Invoke it}} The Dynkin diagram of \(B_3\) is \dynkin{B}{3}. \end{tcblisting} \begin{tcblisting}{title={Inside a \TikZ statement}} -\tikz \dynkin{B}{3}; +The Dynkin diagram of \(B_3\) is +\tikz[baseline=-0.5ex] \dynkin{B}{3}; \end{tcblisting} \begin{tcblisting}{title={Inside a \TikZ environment}} -\begin{tikzpicture} +The Dynkin diagram of \(B_3\) is +\begin{tikzpicture}[baseline=-0.5ex] \dynkin{B}{3} \end{tikzpicture} \end{tcblisting} @@ -441,6 +451,116 @@ For such rare situations, there is an option: \end{tcblisting} +\begingroup +\RenewDocumentCommand\wdtA{}{.35cm} +\RenewDocumentCommand\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 & +\multicolumn{2}{E}{ +\begin{tikzpicture}[baseline=0pt] +\dynkin{A}{o.o*o.o*o.o} +\dynkinLabelRoot{3}{d} +\dynkinLabelRoot{6}{n-d} +\end{tikzpicture} +} +\\ +% 2 +A_n & +\multicolumn{2}{E}{ +\begin{tikzpicture}[baseline=0pt] +\dynkin{A}{o.o*o.o*o.o*o.o*o.o} +\dynkinLabelRoot{3}{d} +\dynkinLabelRoot{6}{rd} +\dynkinLabelRoot{9}{n-rd} +\dynkinLabelRoot{12}{n-d} +\end{tikzpicture} +} +\\ +% 3 +B_n & +\multicolumn{2}{E}{ +\begin{tikzpicture}[baseline=0pt] +\dynkin{B}{**.*.o.oo} +\dynkinLabelRoot{3}{r} +\end{tikzpicture} +} +\\ +% 4 +C_n & +\multicolumn{2}{E}{ +\begin{tikzpicture}[baseline=0pt] +\dynkin{C}{o.o*o.o*o.oo} +\dynkinLabelRoot{3}{d} +\dynkinLabelRoot{6}{rd} +\end{tikzpicture} +} +\\ +% 5 +D_n & +\multicolumn{2}{E}{ +\begin{tikzpicture}[baseline=0pt] +\dynkin{D}{o.o*o.o*o.ooo} +\dynkinLabelRoot{3}{d} +\dynkinLabelRoot{6}{rd} +\end{tikzpicture} +} +\\ +% 6 +E_6 & +\dynk{E}{*oooo*} +% 7 +E_6 & +\dynk{E}{o*o*oo} +% 8 +E_6 & +\dynk{E}{o*oooo} +% 9 +E_6 & +\dynk{E}{**ooo*} +% 10 +E_7 & +\dynk{E}{*oooooo} +% 11 +E_7 & +\dynk{E}{ooooo*o} +% 12 +E_7 & +\dynk{E}{oooooo*} +% 13 +E_7 & +\dynk{E}{*oooo*o} +% 14 - corrected from Springer. +E_7 & +\dynk{E}{*oooo**} +% 15 +E_7 & +\dynk{E}{*o**o*o} +% 16 +E_8 & +\dynk{E}{*ooooooo} +% 17 +E_8 & +\dynk{E}{ooooooo*} +% 18 +E_8 & +\dynk{E}{*oooooo*} +% 19 +E_8 & +\dynk{E}{oooooo**} +% 20 +E_8 & +\dynk{E}{*oooo***} +% 21 +F_4 & +\dynk{F}{ooo*} +% 22 +D_4 & +\dynk{D}{o*oo} +\end{longtable} +\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: @@ -641,7 +761,7 @@ The Dynkin diagrams package has limited support for folding Dynkin diagrams. \end{tcblisting} Some Dynkin diagrams have multiple foldings, which we attempt to distinguish (not entirely successfully) by their \emph{ply}: the maximum number of roots folded together. -Most diagrams can only allow a 2-ply folding, so \verb!fold! is a synonym form \verb!ply=2!. +Most diagrams can only allow a 2-ply folding, so \verb!fold! is a synonym for \verb!ply=2!. \begin{tcblisting}{title={3-ply}} \dynkin[ply=3]{D}{4} @@ -714,7 +834,7 @@ We have to be careful about the 4-ply foldings of \(D^{(1)}_{2\ell}\), for which }% \begin{filecontents*}{DoneTwoElBendy.tex} -\begin{tikzpicture} +\begin{tikzpicture}[baseline=0pt] \dynkin[ply=4]{D}[1]{****.*****.*****} \dynkinFold[bend right=65]{1}{13} \dynkinFold[bend right=65]{0}{14} @@ -723,7 +843,7 @@ We have to be careful about the 4-ply foldings of \(D^{(1)}_{2\ell}\), for which \begin{filecontents*}{DoneTwoElStraight.tex} -\begin{tikzpicture} +\begin{tikzpicture}[baseline=0pt] \dynkin[ply=4]{D}[1]{****.*****.*****} \dynkinFold{0}{1} \dynkinFold{1}{13} @@ -938,9 +1058,9 @@ Below we draw the Vogan diagrams of some affine Lie superalgebras \cite{Ransingh \fi% }% -\tikzset{/Dynkin diagram,labelMacro/.code=\labls{#1},label,radius=.06cm} - +\begingroup +\tikzset{/Dynkin diagram,labelMacro/.code=\labls{#1},label,radius=.06cm} \tcbset{text width=10cm} \RenewDocumentCommand\wdtA{}{2cm} @@ -1171,8 +1291,86 @@ Below we draw the Vogan diagrams of some affine Lie superalgebras \cite{Ransingh \end{tikzpicture}% \end{tcblisting} \end{Category} +\endgroup +\begingroup +\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}}} +\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} +\end{longtable} +\endgroup -- cgit v1.2.3