summaryrefslogtreecommitdiff
path: root/Master/texmf-dist
diff options
context:
space:
mode:
Diffstat (limited to 'Master/texmf-dist')
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/README6
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.bib61
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.pdfbin516997 -> 593579 bytes
-rw-r--r--Master/texmf-dist/doc/latex/dynkin-diagrams/dynkin-diagrams.tex228
-rw-r--r--Master/texmf-dist/tex/latex/dynkin-diagrams/dynkin-diagrams.sty6
5 files changed, 267 insertions, 34 deletions
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
--- 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 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<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}
+\end{longtable}
+\endgroup
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 320b7e60242..2449588637e 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 3.11
+% Version 3.12
%
%
% This package draws Dynkin diagrams in LaTeX documents, using the TikZ package.
@@ -18,7 +18,7 @@
%
%
\NeedsTeXFormat{LaTeX2e}[1994/06/01]
-\ProvidesPackage{dynkin-diagrams}[2018/02/28 Dynkin diagrams]
+\ProvidesPackage{dynkin-diagrams}[2018/04/30 Dynkin diagrams]
\RequirePackage{tikz}
\RequirePackage{xstring}
\RequirePackage{xparse}
@@ -1987,7 +1987,7 @@
{I}{ \global\dynkin@rank=6\gdef\dynkin@string{oooooo}}%
{II} {\global\dynkin@ply=2\gdef\dynkin@string{oooooo}}%
{III}{\global\dynkin@ply=2\gdef\dynkin@string{oo***o}}%
- {IV} {\gdef\dynkin@string{oo***o}}%
+ {IV} {\gdef\dynkin@string{o****o}}%
{V}{ \gdef\dynkin@string{ooooooo}}%
{VI} {\gdef\dynkin@string{o*oo*o*} }%
{VII}{\gdef\dynkin@string{o****oo}}%
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-26 08:50:34 +0000