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authorKarl Berry <karl@freefriends.org>2017-11-18 21:46:02 +0000
committerKarl Berry <karl@freefriends.org>2017-11-18 21:46:02 +0000
commitba6f6ac5705667b8a0d7d3ddcb50a275d06278a1 (patch)
tree3aa4f40ac2adb0053b3e32e9b14958cef33b6c0a /Master/texmf-dist/doc
parent9746eec6f52784c17ea0fdd0c1d47e8deb9ca0f8 (diff)
dynkin-diagrams (18nov17)
git-svn-id: svn://tug.org/texlive/trunk@45846 c570f23f-e606-0410-a88d-b1316a301751
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-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/README4
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib212
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdfbin153870 -> 233754 bytes
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex667
4 files changed, 787 insertions, 96 deletions
diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/README b/Master/texmf-dist/doc/latex/dynkin-diagrams/README
index 0a9ec82779f..26cba041b7c 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
- v1.0
+ v2.0
- 8 September 2017
+ 18 November 2017
___________________________________
Authors : Ben McKay
diff --git a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib
new file mode 100644
index 00000000000..a72cb1dade1
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib
@@ -0,0 +1,212 @@
+% This file was created with JabRef 2.10b2.
+% Encoding: ISO8859_1
+
+
+@Book{Bourbaki:2002,
+ Title = {Lie groups and {L}ie algebras. {C}hapters 4--6},
+ Author = {Bourbaki, Nicolas},
+ Publisher = {Springer-Verlag, Berlin},
+ Year = {2002},
+ Note = {Translated from the 1968 French original by Andrew Pressley},
+ Series = {Elements of Mathematics (Berlin)},
+
+ ISBN = {3-540-42650-7},
+ Mrclass = {17-01 (00A05 20E42 20F55 22-01)},
+ Mrnumber = {1890629},
+ Owner = {user},
+ Pages = {xii+300},
+ Timestamp = {2017.11.15},
+ Url = {https://doi.org/10.1007/978-3-540-89394-3}
+}
+
+@Book{Carter:2005,
+ Title = {Lie algebras of finite and affine type},
+ Author = {Carter, R. W.},
+ Publisher = {Cambridge University Press, Cambridge},
+ Year = {2005},
+ Series = {Cambridge Studies in Advanced Mathematics},
+ Volume = {96},
+
+ ISBN = {978-0-521-85138-1; 0-521-85138-6},
+ Mrclass = {17-02 (17B67)},
+ Mrnumber = {2188930},
+ Mrreviewer = {Stephen Slebarski},
+ Owner = {user},
+ Pages = {xviii+632},
+ Timestamp = {2017.11.15},
+ Url = {https://doi.org/10.1017/CBO9780511614910}
+}
+
+@Book{Dynkin:2000,
+ Title = {Selected papers of {E}. {B}. {D}ynkin with commentary},
+ Author = {Dynkin, E. B.},
+ Publisher = {American Mathematical Society, Providence, RI; International Press, Cambridge, MA},
+ Year = {2000},
+ Note = {Edited by A. A. Yushkevich, G. M. Seitz and A. L. Onishchik},
+
+ ISBN = {0-8218-1065-0},
+ Mrclass = {01A75 (60Jxx)},
+ Mrnumber = {1757976},
+ Mrreviewer = {William M. McGovern},
+ Owner = {user},
+ Pages = {xxviii+796},
+ 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}
+}
+
+@Book{Grove/Benson:1985,
+ Title = {Finite reflection groups},
+ Author = {Grove, L. C. and Benson, C. T.},
+ Publisher = {Springer-Verlag, New York},
+ Year = {1985},
+ Edition = {Second},
+ Series = {Graduate Texts in Mathematics},
+ Volume = {99},
+
+ ISBN = {0-387-96082-1},
+ Mrclass = {20-01 (20B25 20H15)},
+ Mrnumber = {777684},
+ Owner = {user},
+ Pages = {x+133},
+ Timestamp = {2017.11.15},
+ Url = {https://doi.org/10.1007/978-1-4757-1869-0}
+}
+
+@Book{Helgason:2001,
+ Title = {Differential geometry, {L}ie groups, and symmetric spaces},
+ Author = {Helgason, Sigurdur},
+ Publisher = {American Mathematical Society, Providence, RI},
+ Year = {2001},
+ Note = {Corrected reprint of the 1978 original},
+ Series = {Graduate Studies in Mathematics},
+ Volume = {34},
+
+ ISBN = {0-8218-2848-7},
+ Mrclass = {53C35 (22E10 22E46 22E60)},
+ Mrnumber = {1834454},
+ Owner = {user},
+ Pages = {xxvi+641},
+ Timestamp = {2017.11.15},
+ Url = {https://doi.org/10.1090/gsm/034}
+}
+
+@Book{Humphreys:1990,
+ Title = {Reflection groups and {C}oxeter groups},
+ Author = {Humphreys, James E.},
+ Publisher = {Cambridge University Press, Cambridge},
+ Year = {1990},
+ Series = {Cambridge Studies in Advanced Mathematics},
+ Volume = {29},
+
+ ISBN = {0-521-37510-X},
+ Mrclass = {20-02 (20F32 20F55 20G15 20H15)},
+ Mrnumber = {1066460},
+ Mrreviewer = {Louis Solomon},
+ Owner = {user},
+ Pages = {xii+204},
+ Timestamp = {2017.11.15},
+ Url = {https://doi.org/10.1017/CBO9780511623646}
+}
+
+@Book{Kac:1990,
+ Title = {Infinite-dimensional {L}ie algebras},
+ Author = {Kac, Victor G.},
+ Publisher = {Cambridge University Press, Cambridge},
+ Year = {1990},
+ Edition = {Third},
+
+ ISBN = {0-521-37215-1; 0-521-46693-8},
+ Mrclass = {17B65 (17B67 17B68 58F07)},
+ Mrnumber = {1104219},
+ Owner = {user},
+ Pages = {xxii+400},
+ Timestamp = {2017.11.15},
+ Url = {https://doi.org/10.1017/CBO9780511626234}
+}
+
+@Book{OnishchikVinberg:1990,
+ Title = {Lie groups and algebraic groups},
+ Author = {Onishchik, A. L. and Vinberg, {\`E}. B.},
+ Publisher = {Springer-Verlag},
+ Year = {1990},
+
+ Address = {Berlin},
+ Note = {Translated from the Russian and with a preface by D. A. Leites},
+ Series = {Springer Series in Soviet Mathematics},
+
+ ISBN = {3-540-50614-4},
+ Mrclass = {22-01 (17B20 20G20 22E10 22E15)},
+ Mrnumber = {91g:22001},
+ Mrreviewer = {James E. Humphreys},
+ Owner = {user},
+ Pages = {xx+328},
+ Timestamp = {2017.11.15}
+}
+
+@Book{Onishchik/Vinberg:1990,
+ Title = {Lie groups and algebraic groups},
+ Author = {Onishchik, A. L. and Vinberg, \`E. B.},
+ Publisher = {Springer-Verlag, Berlin},
+ Year = {1990},
+ Note = {Translated from the Russian and with a preface by D. A. Leites},
+ Series = {Springer Series in Soviet Mathematics},
+
+ ISBN = {3-540-50614-4},
+ Mrclass = {22-01 (17B20 20G20 22E10 22E15)},
+ Mrnumber = {1064110},
+ Mrreviewer = {James E. Humphreys},
+ Owner = {user},
+ Pages = {xx+328},
+ Timestamp = {2017.11.15},
+ Url = {https://doi.org/10.1007/978-3-642-74334-4}
+}
+
+@Book{Satake:1980,
+ Title = {Algebraic structures of symmetric domains},
+ Author = {Satake, Ichir\^o},
+ Publisher = {Iwanami Shoten, Tokyo; Princeton University Press, Princeton, N.J.},
+ Year = {1980},
+ Series = {Kan\^o Memorial Lectures},
+ Volume = {4},
+
+ Mrclass = {32-02 (17C35 32Mxx 53C35)},
+ Mrnumber = {591460},
+ Mrreviewer = {S. Murakami},
+ Owner = {user},
+ Pages = {xvi+321},
+ Timestamp = {2017.11.15}
+}
+
+@Book{Vinberg:1994,
+ Title = {Lie groups and {L}ie algebras, {III}},
+ Editor = {Vinberg, \`E. B.},
+ Publisher = {Springer-Verlag, Berlin},
+ Year = {1994},
+ Note = {Structure of Lie groups and Lie algebras, A translation of {{\i}t Current problems in mathematics. Fundamental directions. Vol. 41} (Russian), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1990 [ MR1056485 (91b:22001)], Translation by V. Minachin [V. V. Minakhin], Translation edited by A. L. Onishchik and \`E. B. Vinberg},
+ Series = {Encyclopaedia of Mathematical Sciences},
+ Volume = {41},
+
+ ISBN = {3-540-54683-9},
+ Mrclass = {22-06 (17-06 22Exx)},
+ Mrnumber = {1349140},
+ Owner = {user},
+ Pages = {iv+248},
+ Timestamp = {2017.11.15},
+ Url = {https://doi.org/10.1007/978-3-662-03066-0}
+}
+
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 fa4ed5acbe9..851c6ae2200 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 7bc9eb0a18d..f6566c0be0e 100644
--- a/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex
+++ b/Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex
@@ -3,124 +3,197 @@
\title{The Dynkin diagrams package}
\author{Ben McKay}
\date{\today}
-
-\usepackage{dynkin-diagrams}
+
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{array}
\usepackage{xstring}
-\usepackage{etoolbox}
+\usepackage{etoolbox}
+\usepackage{longtable}
+\usepackage{showexpl}
+\usepackage{booktabs}
+\usepackage{dynkin-diagrams}
\usetikzlibrary{backgrounds}
\usetikzlibrary{decorations.markings}
-\usepackage{longtable}
-\usepackage{showexpl}
\newcommand{\C}[1]{\mathbb{C}^{#1}}
-
-
\renewcommand*{\arraystretch}{1.5}
+\renewcommand\ResultBox{\fcolorbox{gray!50}{gray!30}}
+
\begin{document}
+
\maketitle
\tableofcontents
-\section{Quick introduction}
+\section{Quick introduction}
This is a test of the Dynkin diagram package.
Load the package via
\begin{verbatim}
-\usepackage{dynkin-diagrams}
+\usepackage{dynkin-diagrams}
\end{verbatim}
-and invoke it directly:
+(see below for options) and invoke it directly:
+
\begin{LTXexample}
The flag variety of pointed lines in
projective 3-space is associated to
-the Dykin diagram \dynk[parabolic=3]{A}{3}.
+the Dynkin diagram \dynkin[parabolic=3]{A}{3}.
\end{LTXexample}
-or use the long form inside a \verb!\tikz! statement or environment:
+
+or use the long form inside a \verb!\tikz! statement:
\begin{LTXexample}
\tikz \dynkin[parabolic=3]{A}{3};
\end{LTXexample}
+
+or a TikZ environment:
+\begin{LTXexample}
+\begin{tikzpicture}
+\dynkin[parabolic=3,label]{A}{3}
+\end{tikzpicture}
+\end{LTXexample}
With labels for the roots:
\begin{LTXexample}
-\tikz \dynkin[parabolic=3,label=true]{A}{3};
+\dynkin[parabolic=3,label]{A}{3}
\end{LTXexample}
-
-\bigskip
-
-Inside an environment:
+\newpage\noindent%
+Make up your own labels for the roots:
\begin{LTXexample}
\begin{tikzpicture}
-\dynkin[parabolic=3,label=true]{A}{3}
+\dynkin[parabolic=3]{A}{3}
+\rootlabel{2}{\alpha_2}
\end{tikzpicture}
\end{LTXexample}
-
-\bigskip
-
-Make up your own labels for the roots:
-
+Use any text scale you like:
+\begin{LTXexample}
+\begin{tikzpicture}
+\dynkin[parabolic=3,textscale=1.2]{A}{3};
+\rootlabel{2}{\alpha_2}
+\end{tikzpicture}
+\end{LTXexample}
+and access root labels via TikZ:
\begin{LTXexample}
\begin{tikzpicture}
\dynkin[parabolic=3]{A}{3};
-\node at (root label 2) {\scalebox{.7}{\(\alpha_2\)}};
+\node at (root label 2) {\(\alpha_2\)};
\end{tikzpicture}
\end{LTXexample}
-
-\newpage
-
-Drawing curves between the roots:
-
+The labels have default locations:
\begin{LTXexample}
\begin{tikzpicture}
-\dynkin[parabolic=429]{E}{8}
-\draw[brown,-latex]
- (root 3.south)
- to [out=-90, in=-90]
- (root 6.south);
+\dynkin{E}{8};
+\rootlabel{1}{\alpha_1}
+\rootlabel{2}{\alpha_2}
+\rootlabel{3}{\alpha_3}
\end{tikzpicture}
\end{LTXexample}
-
-Various options:
-
+You can use a starred form to flip labels to alternate locations:
\begin{LTXexample}
-\tikz \dynkin[color=brown]{G}{2};
+\begin{tikzpicture}
+\dynkin{E}{8};
+\rootlabel*{1}{\alpha_1}
+\rootlabel*{2}{\alpha_2}
+\rootlabel*{3}{\alpha_3}
+\end{tikzpicture}
\end{LTXexample}
-
+TikZ can access the roots themselves:
+\typeout{AAAAAAA}
\begin{LTXexample}
-\tikz \dynkin[edgelength=1.2,parabolic=3]{A}{3};
+\begin{tikzpicture}
+\dynkin{A}{4};
+\fill[white,draw=black] (root 2) circle (.1cm);
+\draw[black] (root 2) circle (.05cm);
+\end{tikzpicture}
\end{LTXexample}
-
+Some diagrams will have double edges:
\begin{LTXexample}
-\tikz \dynkin[crosssize=.1cm,parabolic=3]{A}{3};
+\dynkin{F}{4}
\end{LTXexample}
-
+or triple edges:
\begin{LTXexample}
-\tikz \dynkin[dotradius=.08cm,parabolic=3]{A}{3};
+\dynkin{G}{2}
\end{LTXexample}
-
+\newpage\noindent%
+Draw curves between the roots:
\begin{LTXexample}
-\begin{tikzpicture}[
- show background rectangle,
- background rectangle/.style={fill=lightgray}]
-\dynkin[parabolic=1,background color=lightgray]{G}{2}
+\begin{tikzpicture}
+\dynkin[parabolic=429]{E}{8}
+\draw[very thick, black!50,-latex] (root 3.south) to [out=-45, in=-135] (root 6.south);
\end{tikzpicture}
\end{LTXexample}
-
-
-\section{Syntax}
-
-Inside a \verb!\tikz! environment, the syntax is \verb!\dynkin[<options>]{<letter>}{<rank>}! where \verb!<letter>! is \(A,B,C,D,E,F\) or \(G\), the family of root system for the Dynkin diagram, and \verb!<rank>! is an integer representing the rank, or is the symbol \verb!*! to represent an indefinite rank:
-
+Draw dots on the roots:
\begin{LTXexample}
\begin{tikzpicture}
-\dynkin[parabolic=5]{D}{*}
+\dynkin[label]{C}{8}
+\dynkinopendot{3}
+\dynkinopendot{7}
\end{tikzpicture}
\end{LTXexample}
+Colours:
+\begin{LTXexample}
+\dynkin[color=blue!50,backgroundcolor=red!20]{G}{2}
+\end{LTXexample}
+Edge lengths:
+\begin{LTXexample}
+\dynkin[edgelength=1.2,parabolic=3]{A}{3}
+\end{LTXexample}
+Sizes of dots and crosses:
+\begin{LTXexample}
+\dynkin[dotradius=.08cm,parabolic=3]{A}{3}
+\end{LTXexample}
+Edge styles:
+\begin{LTXexample}
+\dynkin[edge=very thick,parabolic=3]{A}{3}
+\end{LTXexample}
+Open circles instead of closed dots:
+\begin{LTXexample}
+\dynkin[open]{E}{8}
+\end{LTXexample}
+Add closed dots to the open circles, at roots in the current ordering:
+\begin{LTXexample}
+\begin{tikzpicture}
+\dynkin[open]{E}{8};
+\dynkincloseddot{5}
+\dynkincloseddot{8}
+\end{tikzpicture}
+\end{LTXexample}
+More colouring:
+\begin{LTXexample}
+\begin{tikzpicture}[show background rectangle,
+ background rectangle/.style={fill=red!10}]
+\dynkin[parabolic=1,backgroundcolor=blue!20]{G}{2}
+\end{tikzpicture}
+\end{LTXexample}
+Cross styles:
+\begin{LTXexample}
+\dynkin[parabolic=124,cross=thin]{E}{8}
+\end{LTXexample}
+\newpage\noindent{}
+Suppress arrows:
+\begin{LTXexample}
+\dynkin[arrows=false]{F}{4}
+\end{LTXexample}
+\begin{LTXexample}
+\dynkin[arrows=false]{G}{2}
+\end{LTXexample}
-Outside a \verb!\tikz! environment, use \verb!\dynk! instead of \verb!\dynkin!.
+\section{Syntax}
+The syntax is \verb!\dynkin[<options>]{<letter>}{<rank>}! where \verb!<letter>! is \(A,B,C,D,E,F\) or \(G\), the family of root system for the Dynkin diagram, and \verb!<rank>! is an integer representing the rank, or is the symbol \verb!*! to represent an indefinite rank:
+\begin{LTXexample}
+\dynkin[edge=thick,edgelength=.5cm]{A}{*}
+\end{LTXexample}
+\begin{LTXexample}
+\dynkin[edge=thick,edgelength=.5cm]{B}{*}
+\end{LTXexample}
+\begin{LTXexample}
+\dynkin[edge=thick,edgelength=.5cm]{C}{*}
+\end{LTXexample}
+\begin{LTXexample}
+\dynkin[edge=thick,edgelength=.5cm]{D}{*}
+\end{LTXexample}
+Outside a TikZ environment, the command builds its own TikZ environment.
-\bigskip
\newcommand*{\typ}[1]{\(\left<\texttt{#1}\right>\)}
\newcommand*{\optionLabel}[3]{%%
@@ -128,37 +201,108 @@ Outside a \verb!\tikz! environment, use \verb!\dynk! instead of \verb!\dynkin!.
}%%
\section{Options}
+\par\noindent{}All \verb!\dynkin! options (except \texttt{affine}, \texttt{folded}, \texttt{label} and \texttt{parabolic} ) can also be passed to the package to force a global default option:
+\par\noindent%
+\begin{verbatim}
+\usepackage[
+ ordering=Kac,
+ color=blue,
+ open,
+ dotradius=.06cm,
+ backgroundcolor=red]
+ {dynkin-diagrams}
+\end{verbatim}
\par\noindent%
\begin{tabular}{p{1cm}p{10cm}}
\optionLabel{parabolic}{\typ{integer}}{0}
& A parabolic subgroup with specified integer, where the integer
is computed as \(n=\sum 2^i a_i\), \(a_i=0\) or \(1\), to say that root \(i\) is crossed, i.e. a noncompact root. \\
\optionLabel{color}{\typ{color name}}{black} \\
-\optionLabel{background color}{\typ{color name}}{white}
+\optionLabel{backgroundcolor}{\typ{color name}}{white}
& This only says what color you have already set for the background rectangle. It is needed precisely for the \(G_2\) root system, to draw the triple line correctly, and only when your background color is not white. \\
-\optionLabel{dotradius}{\typ{number}cm}{.04cm}
-& size of the dots in the Dynkin diagram \\
+\optionLabel{dotradius}{\typ{number}cm}{.05cm}
+& size of the dots and of the crosses in the Dynkin diagram \\
\optionLabel{edgelength}{\typ{number}cm}{.35cm}
& distance between nodes in the Dynkin diagram \\
-\optionLabel{crosssize}{\typ{number}}{1.5}
-& size of the crosses, for parabolic subgroup diagrams. \\
+\optionLabel{edge}{\typ{TikZ style data}}{thin}
+& style of edges in the Dynkin diagram \\
+\optionLabel{open}{\typ{true or false}}{false}
+& use open circles rather than solid dots as default \\
\optionLabel{label}{true or false}{false}
& whether to label the roots by their root numbers. \\
+\optionLabel{arrows}{\typ{true or false}}{true}
+& whether to draw the arrows that arise along the edges. \\
+\optionLabel{folded}{\typ{true or false}}{true}
+& whether, when drawing \(A\), \(D\) or \(E_6\) diagrams, to draw them folded. \\
+\optionLabel{foldarrowstyle}{\typ{TikZ style}}{stealth-stealth}
+& when drawing folded diagrams, style for the fold arrows. \\
+\optionLabel{foldarrowcolor}{\typ{colour}}{black!50}
+& when drawing folded diagrams, colour for the fold arrows. \\
+\optionLabel{Coxeter}{\typ{true or false}}{false}
+& whether to draw a Coxeter diagram, rather than a Dynkin diagram. \\
+
+\optionLabel{ordering}{\typ{Adams, Bourbaki, Carter, Dynkin, Kac}}{Bourbaki}
+& which ordering of the roots to use in exceptional root systems as follows:
\end{tabular}
-%% All other options are passed to tikz.
-\section{Finding the roots}
-The roots are labelled in the Bourbaki labelling, but from \(0\) to \(r-1\), where \(r\) is the rank.
-The command sets up nodes \texttt{(root 0)}, \texttt{(root 1)}, and so on.
-Use these tikz nodes to draw on the Dynkin diagram.
-It also sets up nodes \texttt{(root label 0)}, \texttt{(root label 1)}, and so on for the labels.
+\newpage
+
+\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}
+\\
+}%
+
+\begin{center}
+\begin{longtable}{@{}llllll@{}}
+\toprule
+& Adams & Bourbaki & Carter & Dynkin & Kac \\ \midrule
+\endfirsthead
+\toprule
+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}
+\end{longtable}
+\end{center}
+\par\noindent{}All other options are passed to TikZ.
+
+\section{Finding the roots}
+The roots are labelled from \(1\) to \(r\), where \(r\) is the rank.
+The command sets up TikZ nodes \texttt{(root 1)}, \texttt{(root 2)}, and so on.
+Affine extended Dynkin diagrams have affine root are at \texttt{(root 0)}.
+Use these tikz nodes to draw on the Dynkin diagram, as above.
+It also sets up TikZ nodes \texttt{(root label 0)}, \texttt{(root label 1)}, and so on for the labels, and TikZ nodes \texttt{(root label swap 0)}, \texttt{(root label swap 1)}, and so on as alternative label locations, in case you want two labels on the same root, or the default choice doesn't look the way you like.
+\begin{LTXexample}
+\begin{tikzpicture}
+\dynkin{E}{6};
+\rootlabel{2}{\alpha_2}
+\rootlabel{5}{\alpha_5}
+\end{tikzpicture}
+\end{LTXexample}
\section{Example: some parabolic subgroups}
-\newcommand{\drawparabolic}[3]%%
-{#1_{#2,#3} & \tikz \dynkin[parabolic=#3]{#1}{#2}; \\}
+\newcommand{\drawparabolic}[3]{#1_{#2,#3} & \tikz \dynkin[parabolic=#3]{#1}{#2}; \\}
\begin{center}
\begin{longtable}{@{}>{$}r<{$}m{2cm}m{2cm}@{}}
@@ -167,18 +311,22 @@ It also sets up nodes \texttt{(root label 0)}, \texttt{(root label 1)}, and so o
\endfoot
\endlastfoot
\drawparabolic{A}{1}{0}
-\drawparabolic{A}{1}{1}
+\drawparabolic{A}{1}{2}
\drawparabolic{A}{2}{0}
\drawparabolic{A}{2}{2}
-\drawparabolic{A}{2}{2}
-\drawparabolic{B}{2}{3}
-\drawparabolic{C}{3}{5}
-\drawparabolic{D}{5}{4}
-\drawparabolic{E}{6}{5}
-\drawparabolic{E}{7}{101}
-\drawparabolic{E}{8}{123}
-\drawparabolic{F}{4}{13}
+\drawparabolic{A}{2}{4}
+\drawparabolic{A}{2}{6}
+\drawparabolic{B}{2}{6}
+\drawparabolic{C}{3}{10}
+\drawparabolic{D}{5}{8}
+\drawparabolic{E}{6}{10}
+\drawparabolic{E}{7}{202}
+\drawparabolic{E}{8}{246}
+\drawparabolic{F}{4}{26}
+\drawparabolic{G}{2}{0}
\drawparabolic{G}{2}{2}
+\drawparabolic{G}{2}{4}
+\drawparabolic{G}{2}{6}
\end{longtable}
\end{center}
@@ -188,24 +336,355 @@ It also sets up nodes \texttt{(root label 0)}, \texttt{(root label 1)}, and so o
\renewcommand*{\arraystretch}{1.5}
\begin{center}
-\begin{longtable}{@{}>{$}r<{$}m{2cm}m{5cm}@{}}
+\begin{longtable}{@{}>{$}r<{$}m{2.2cm}m{5cm}@{}}
\endfirsthead
\endhead
\endfoot
\endlastfoot
- A_n &\dynk[parabolic=8]{A}{*}& Grassmannian of $k$-planes in $\C{n+1}$ \\
- B_n &\dynk[parabolic=1]{B}{*}& $(2n-1)$-dimensional hyperquadric, i.e. the variety of null lines in $\C{2n+1}$
- \\
- C_n &\dynk[parabolic=16]{C}{*}& space of Lagrangian $n$-planes in $\C{2n}$
- \\
- D_n &\dynk[parabolic=1]{D}{*}&$(2n-2)$-dimensional hyperquadric, i.e. the variety of null lines in $\C{2n}$
-\\
- D_n&\dynk[parabolic=32]{D}{*}& one component of the variety of maximal dimension null subspaces of $\C{2n}$ \\
- D_n
- &\dynk[parabolic=16]{D}{*}&the other component\\
- E_6&\dynk[parabolic=1]{E}{6}&complexified octave projective plane\\
- E_6&\dynk[parabolic=32]{E}{6}&its dual plane\\
- E_7 &\dynk[parabolic=64]{E}{7}& the space of null octave 3-planes in octave 6-space
+ A_n &
+ \dynkin[parabolic=16]{A}{*} &
+ Grassmannian of $k$-planes in $\C{n+1}$
+ \\
+ B_n &
+ \dynkin[parabolic=2]{B}{*} &
+ $(2n-1)$-dimensional hyperquadric, i.e. the variety of null lines in $\C{2n+1}$
+ \\
+ C_n &
+ \dynkin[parabolic=32]{C}{*} &
+ space of Lagrangian $n$-planes in $\C{2n}$
+ \\
+ D_n &
+ \dynkin[parabolic=2]{D}{*} &
+ $(2n-2)$-dimensional hyperquadric, i.e. the variety of null lines in $\C{2n}$
+ \\
+ D_n &
+ \dynkin[parabolic=64]{D}{*} &
+ one component of the variety of maximal dimension null subspaces of $\C{2n}$ \\
+ D_n &
+ \dynkin[parabolic=32]{D}{*} &
+ the other component\\
+ E_6 &
+ \dynkin[parabolic=2]{E}{6} &
+ complexified octave projective plane\\
+ E_6 &
+ \dynkin[parabolic=64]{E}{6}&its dual plane\\
+ E_7 &
+ \dynkin[parabolic=128]{E}{7}& the space of null octave 3-planes in octave 6-space
\end{longtable}
\end{center}
+
+
+\section{Affine extended Dynkin diagrams}
+
+\begin{LTXexample}
+\dynkin[affine,edge=thick]{A}{*}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[edgelength=1cm,edge=thick,affine]{A}{*}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[scale=1.5,edge=thick,affine]{A}{*}
+\end{LTXexample}
+
+
+\begin{LTXexample}
+\begin{tikzpicture}
+\dynkin[affine,label]{A}{8};
+\end{tikzpicture}
+\end{LTXexample}
+
+
+\begin{LTXexample}
+\begin{tikzpicture}
+\dynkin[affine]{A}{*};
+\node at (root label 0) {\(\alpha_0\)};
+\end{tikzpicture}
+\end{LTXexample}
+
+\begin{LTXexample}
+\begin{tikzpicture}
+\dynkin[affine]{A}{9}
+\node at (root label 0) {\(\alpha_0\)};
+\end{tikzpicture}
+\end{LTXexample}
+
+You can use TikZ to put in labels:
+
+\begin{LTXexample}
+\begin{tikzpicture}
+\dynkin[affine]{A}{9};
+\node at (root label 0) {\(\alpha_0\)};
+\node at (root label 1) {\(\alpha_1\)};
+\node at (root label 2) {\(\alpha_2\)};
+\node at (root label 3) {\(\alpha_3\)};
+\end{tikzpicture}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{A}{1}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{B}{8}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{B}{*}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{C}{8}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{C}{*}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{D}{8}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{D}{*}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{E}{6}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{E}{7}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{E}{8}
+\end{LTXexample}
+
+Open circles instead of closed dots:
+\begin{LTXexample}
+\dynkin[affine,open,label]{E}{8}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{F}{4}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[affine,label]{G}{2}
+\end{LTXexample}
+
+
+\section{Coxeter diagrams}
+
+\begin{LTXexample}
+\dynkin[Coxeter]{B}{7}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[Coxeter]{F}{4}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[Coxeter]{G}{2}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[Coxeter]{H}{7}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[Coxeter]{I}{7}
+\end{LTXexample}
+
+
+\section{Folded Dynkin diagrams}
+
+\begin{LTXexample}
+\dynkin[folded]{E}{6}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{E}{6}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded]{A}{*}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{A}{1}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{A}{2}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{A}{3}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{A}{4}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{A}{10}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{A}{11}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label,arrows=false]{A}{11}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded]{D}{*}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{D}{1}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{D}{2}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{D}{3}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{D}{4}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{D}{10}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin[folded,label]{D}{11}
+\end{LTXexample}
+
+
+
+\section{Satake diagrams}
+
+We have incomplete support for Satake diagrams as yet, following the conventions of \cite{Helgason:2001}.
+
+\begin{LTXexample}
+\dynkin{A}{I}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{A}{II}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{E}{I}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{E}{II}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{E}{III}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{E}{IV}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{E}{V}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{E}{VI}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{E}{VII}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{E}{VIII}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{E}{XI}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{F}{I}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{F}{II}
+\end{LTXexample}
+
+\begin{LTXexample}
+\dynkin{G}{I}
+\end{LTXexample}
+
+\begin{LTXexample}
+\begin{tikzpicture}
+\dynkin[open]{E}{6}
+\draw[\dynkinfoldarrowstyle,\dynkinfoldarrowcolor]
+ (root 1.south) to [out=-45, in=-135] (root 6.south);
+\draw[\dynkinfoldarrowstyle,\dynkinfoldarrowcolor]
+ (root 3.south) to [out=-45, in=-135] (root 5.south);
+\end{tikzpicture}
+\end{LTXexample}
+
+\begin{LTXexample}
+\begin{tikzpicture}
+\dynkin[open]{E}{6}
+\dynkincloseddot{3}
+\dynkincloseddot{4}
+\dynkincloseddot{5}
+\draw[\dynkinfoldarrowstyle,\dynkinfoldarrowcolor]
+ (root 1.south) to [out=-45, in=-135] (root 6.south);
+\end{tikzpicture}
+\end{LTXexample}
+
+\section{Other stuff}
+
+Some sophisticated diagrams:
+\begin{center}
+\begin{tikzpicture}
+\dynkin[folded]{D}{9}
+\foreach \i in {2,6,8,9} {
+ \dynkinopendot{\i}
+}
+\dynkinline[white]{4}{5}
+\dynkindots{4}{5}
+\dynkinopendot{4}
+\dynkincloseddot{5}
+\end{tikzpicture}
+\end{center}
+can be drawn using sending TikZ options to \verb!\dynkinline! to erase the old edge, \verb!\dynkindots! to make indefinite edges, and then redrawing the roots next to any edge we draw:
+\begin{LTXexample}
+\begin{tikzpicture}[show background rectangle,
+ background rectangle/.style={fill=red!10}]
+\dynkin[folded]{D}{9};
+\foreach \i in {2,6,8,9} {
+ \dynkinopendot{\i}
+}
+\dynkinline[red!10]{4}{5}
+\dynkindots{4}{5}
+\dynkinopendot{4}
+\dynkincloseddot{5}
+\end{tikzpicture}
+\end{LTXexample}
+
+Always draw roots after edges.
+
+\nocite{*}
+\bibliographystyle{amsplain}
+\bibliography{dynkin-diagrams}
\end{document}