Drawing A2xA2 Dynkin diagram with dynkin-diagrams

diagrams

This is a follow up question: How do I draw it exactly as in the blackboard picture I provide, that is with ellipses around the nodes and for the bottom one with the connections to the rightmost node straight not curved.

I posted it as a comment first but I am not sure people notice when comments are added. Thanks a lot.

Edit: here is minimal working example

\documentclass[12pt]{amsbook}

\usepackage{dynkin-diagrams}

\begin{document}
 
 Question: how do I produced a diagram which only keeps the square in this diagram 
 \dynkin[fold] A{*****}? I.e. a Satake-Tits diagram of type A2xA2 but I do not want to have just \dynkin A2 \dynkin A2 but have the nodes paired up. 

\end{document}

I am using the excellent package Dynkin-diagram .sty
and drawing the diagrams for the non-split version of the Freudenthal-Tits magic square.
I managed to draw all but one of them. In picture below the bottom one
can easily be drawn with

\dynkin[fold] A{*****}

My question is how do I draw the top one? Thanks a lot

Addition: Benjamin Kindly offered to include FTMS non-split into his package. The others I managed to draw, here the output as well as latex code which produces it

\documentclass[12pt]{amsbook}
\usepackage[dvipsnames,table]{xcolor}
\usepackage{dynkin-diagrams}


\begin{document}
 
\begin{center}
\Large
\begin{tabular}{| c | c | c | c | c |}\hline
\cellcolor{lightgray!90} $\mathbb{A}\setminus \mathbb{B}$ &  \cellcolor{lightgray!90} $\mathbb{K}$  & \cellcolor{lightgray!90} $\mathbb{L}$   & \cellcolor{lightgray!90} $\mathbb{H}$ & \cellcolor{lightgray!90} $\mathbb{O}$  \\ \hline
\cellcolor{lightgray!90} $\mathbb{K}$ &  \cellcolor{BurntOrange!80} \dynkin A1  & \cellcolor{BurntOrange!80}  \dynkin A{*o}   & \cellcolor{BurntOrange!80} \dynkin C{o*o} & \cellcolor{BurntOrange!80} \dynkin F{*ooo}  \\ \hline
\cellcolor{lightgray!90} $\mathbb{L}$ &  \cellcolor{SeaGreen} \dynkin A{**}  & \cellcolor{SeaGreen} \begin{dynkinDiagram}[name=upper]A2
\node (current) at ($(upper root 1)+(0,-.35cm)$) {};
\dynkin[at=(current),name=lower]A2
\begin{pgfonlayer}{Dynkin behind}
\foreach \i in {1,2}{%
\draw[/Dynkin diagram/fold style] ($(upper root \i)$) -- ($(lower root \i)$);}
\end{pgfonlayer}
\end{dynkinDiagram}& \cellcolor{SeaGreen} \dynkin A{*ooo*} & \cellcolor{SeaGreen} \dynkin E{*oooo*}\\ \hline
\cellcolor{lightgray!90} $\mathbb{H}$  &  \cellcolor{RoyalBlue!50} \dynkin C{***}  & \cellcolor{RoyalBlue!50} \dynkin[fold] A{*****} & \cellcolor{RoyalBlue!50} \dynkin D{*oo*o*} & \cellcolor{RoyalBlue!50} \dynkin E{*oooo**}\\ \hline
\cellcolor{lightgray!90} $\mathbb{O}$ &  \cellcolor{OrangeRed!70} \dynkin F{****}  &  \cellcolor{OrangeRed!70} \begin{dynkinDiagram}[mark=o]E{II} \dynkinRootMark{*}1
\dynkinRootMark{*}3 \dynkinRootMark{*}5 \dynkinRootMark{*}6 \dynkinRootMark{*}2 \dynkinRootMark{*}4 \end{dynkinDiagram}

& \cellcolor{OrangeRed!70} \dynkin[backwards] E{*o**oo*o} & \cellcolor{Red} ${\color{white} \dynkin E{*oooo***}}$\\ \hline
\end{tabular}
\end{center}

\end{document}

Also here are the diagrams as made in Keynote, they are drawn to emphasize the residual property, namely taking a point residue (covering a dot if you are unfamiliar with buildings language) in a picture yields the one above when going from row 4 to 3, row 3 to 2 (row 2 to 1 is different and uses folding)

Best Answer

Connecting diagrams is described in §28 of the Dynkin Diagrams Package documentation.

You can adjust the vertical space between upper and lower by changing the -.3cm in the code below:

\documentclass[12pt]{amsbook}

\usepackage{dynkin-diagrams}

\begin{document}

Is this:
\begin{dynkinDiagram}[name=upper]A2
\node (current) at ($(upper root 1)+(0,-.3cm)$) {};
\dynkin[at=(current),name=lower]A2
\begin{pgfonlayer}{Dynkin behind}
\foreach \i in {1,2}{%
\draw[/Dynkin diagram/fold style] ($(upper root \i)$) -- ($(lower root \i)$);}
\end{pgfonlayer}
\end{dynkinDiagram}
what you want?

\end{document}

Related Solutions

[Tex/LaTex] How to replicate affine Dynkin diagrams in Kac’s textbook

And now let me show you the right way to do it.

\documentclass{article}
\pagestyle{empty}
\usepackage[paperheight=40cm,scale=.97]{geometry}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage{tikz}
\usetikzlibrary{chains}

\tikzset{node distance=2em, ch/.style={circle,draw,on chain,inner sep=2pt},chj/.style={ch,join},every path/.style={shorten >=4pt,shorten <=4pt},line width=1pt,baseline=-1ex}

\newcommand{\alabel}[1]{%
  \(\alpha_{\mathrlap{#1}}\)
}

\newcommand{\mlabel}[1]{%
  \(#1\)
}

\let\dlabel=\alabel
\let\ulabel=\mlabel

\newcommand{\dnode}[2][chj]{%
\node[#1,label={below:\dlabel{#2}}] {};
}

\newcommand{\dnodea}[3][chj]{%
\dnode[#1,label={above:\ulabel{#2}}]{#3}
}

\newcommand{\dnodeanj}[2]{%
\dnodea[ch]{#1}{#2}
}

\newcommand{\dnodenj}[1]{%
\dnode[ch]{#1}
}

\newcommand{\dnodebr}[1]{%
\node[chj,label={below right:\dlabel{#1}}] {};
}

\newcommand{\dnoder}[2][chj]{%
\node[#1,label={right:\dlabel{#2}}] {};
}

\newcommand{\dydots}{%
\node[chj,draw=none,inner sep=1pt] {\dots};
}

\newcommand{\QRightarrow}{%
\begingroup
\tikzset{every path/.style={}}%
\tikz \draw (0,3pt) -- ++(1em,0) (0,1pt) -- ++(1em+1pt,0) (0,-1pt) -- ++(1em+1pt,0) (0,-3pt) -- ++(1em,0) (1em-1pt,5pt) to[out=-75,in=135] (1em+2pt,0) to[out=-135,in=75] (1em-1pt,-5pt);
\endgroup
}

\newcommand{\QLeftarrow}{%
\begingroup
\tikz
\draw[shorten >=0pt,shorten <=0pt] (0,3pt) -- ++(-1em,0) (0,1pt) -- ++(-1em-1pt,0) (0,-1pt) -- ++(-1em-1pt,0) (0,-3pt) -- ++(-1em,0) (-1em+1pt,5pt) to[out=-105,in=45] (-1em-2pt,0) to[out=-45,in=105] (-1em+1pt,-5pt);
\endgroup
}

\begin{document}
\begin{align*}
A_l &&& 
\begin{tikzpicture}[start chain]
\dnode{1}
\dnode{2}
\dydots
\dnode{l-1}
\dnode{l}
\end{tikzpicture}
&&
(l+1) \\
%
B_l &&&
\begin{tikzpicture}[start chain]
\dnode{1}
\dnode{2}
\dydots
\dnode{l-1}
\dnodenj{l}
\path (chain-4) -- node[anchor=mid] {\(\Rightarrow\)} (chain-5);
\end{tikzpicture}
&&
(2) \\
%
C_l &&&
\begin{tikzpicture}[start chain]
\dnode{1}
\dnode{2}
\dydots
\dnode{l-1}
\dnodenj{l}
\path (chain-4) -- node[anchor=mid] {\(\Leftarrow\)} (chain-5);
\end{tikzpicture}
&&
(2) \\
%
D_l &&&
\begin{tikzpicture}
\begin{scope}[start chain]
\dnode{1}
\dnode{2}
\node[chj,draw=none] {\dots};
\dnode{l-2}
\dnode{l-1}
\end{scope}
\begin{scope}[start chain=br going above]
\chainin(chain-4);
\dnodebr{l}
\end{scope}
\end{tikzpicture}
&&
(4) \\
%
E_6 &&&
\begin{tikzpicture}
\begin{scope}[start chain]
\foreach \dyni in {1,...,5} {
\dnode{\dyni}
}
\end{scope}
\begin{scope}[start chain=br going above]
\chainin (chain-3);
\dnodebr{6}
\end{scope}
\end{tikzpicture}
&&
(3) \\
%
E_7 &&&
\begin{tikzpicture}
\begin{scope}[start chain]
\foreach \dyni in {1,...,6} {
\dnode{\dyni}
}
\end{scope}
\begin{scope}[start chain=br going above]
\chainin (chain-3);
\dnodebr{7}
\end{scope}
\end{tikzpicture}
&&
(2) \\
%
E_8 &&&
\begin{tikzpicture}
\begin{scope}[start chain]
\foreach \dyni in {1,...,7} {
\dnode{\dyni}
}
\end{scope}
\begin{scope}[start chain=br going above]
\chainin (chain-5);
\dnodebr{8}
\end{scope}
\end{tikzpicture}
&&
(1) \\
%
F_4 &&&
\begin{tikzpicture}[start chain]
\dnode{1}
\dnode{2}
\dnodenj{3}
\dnode{4}
\path (chain-2) -- node[anchor=mid] {\(\Rightarrow\)} (chain-3);
\end{tikzpicture}
&&
(1) \\
%
G_2 &&&
\begin{tikzpicture}[start chain]
\dnodenj{1}
\dnodenj{2}
\path (chain-1) -- node {\(\Rrightarrow\)} (chain-2);
\end{tikzpicture}
\end{align*}

\let\dlabel=\mlabel

\begin{align*}
&A_1^{(1)} &&
\begin{tikzpicture}[start chain]
\dnodenj{1}
\dnodenj{1}
\path (chain-1) -- node[anchor=mid] {\(\Longleftrightarrow\)} (chain-2);
\end{tikzpicture}
\\
%
&A_l^{(1)} (l \ge 2) &&
\begin{tikzpicture}[start chain,node distance=1ex and 2em]
\dnode{1}
\dnode{1}
\dydots
\dnode{1}
\dnode{1}
\begin{scope}[start chain=br going above]
\chainin(chain-3);
\node[ch,join=with chain-1,join=with chain-5,label={[inner sep=1pt]10:\(1\)}] {};
\end{scope}
\end{tikzpicture}
\\
%
&B_l^{(1)} (l \ge 3) &&
\begin{tikzpicture}
\begin{scope}[start chain]
\dnode{1}
\dnode{2}
\dnode{2}
\dydots
\dnode{2}
\dnodenj{2}
\end{scope}
\begin{scope}[start chain=br going above]
\chainin(chain-2);
\dnodebr{1}
\end{scope}
\path (chain-5) -- node{\(\Rightarrow\)} (chain-6);
\end{tikzpicture}
\\
%
&C_l^{(1)} (l \ge 2) &&
\begin{tikzpicture}[start chain]
\dnodenj{1}
\dnodenj{2}
\dydots
\dnode{2}
\dnodenj{1}
\path (chain-1) -- node{\(\Rightarrow\)} (chain-2);
\path (chain-4) -- node{\(\Leftarrow\)} (chain-5);
\end{tikzpicture}
\\
%
&D_l^{(1)} (l \ge 4) &&
\begin{tikzpicture}
\begin{scope}[start chain]
\dnode{1}
\dnode{2}
\dnode{2}
\dydots
\dnode{2}
\dnode{1}
\end{scope}
\begin{scope}[start chain=br going above]
\chainin(chain-2);
\dnodebr{1};
\end{scope}
\begin{scope}[start chain=br2 going above]
\chainin(chain-5);
\dnodebr{1};
\end{scope}
\end{tikzpicture}
\\
%
&G_2^{(1)} &&
\begin{tikzpicture}[start chain]
\dnode{1}
\dnode{2}
\dnodenj{3}
\path (chain-2) -- node{\(\Rrightarrow\)} (chain-3);
\end{tikzpicture}
\\
%
&F_4^{(1)} &&
\begin{tikzpicture}[start chain]
\dnode{1}
\dnode{2}
\dnode{3}
\dnodenj{4}
\dnode{2}
\path (chain-3) -- node[anchor=mid]{\(\Rightarrow\)} (chain-4);
\end{tikzpicture}
\\
%
&E_6^{(1)} &&
\begin{tikzpicture}
\begin{scope}[start chain]
\foreach \dyi in {1,2,3,2,1} {
\dnode{\dyi}
}
\end{scope}
\begin{scope}[start chain=br going above]
\chainin(chain-3);
\dnodebr{2}
\dnodebr{1}
\end{scope}
\end{tikzpicture}
\\
%
&E_7^{(1)} &&
\begin{tikzpicture}
\begin{scope}[start chain]
\foreach \dyi in {1,2,3,4,3,2,1} {
\dnode{\dyi}
}
\end{scope}
\begin{scope}[start chain=br going above]
\chainin(chain-4);
\dnodebr{2}
\end{scope}
\end{tikzpicture}
\\
%
&E_8^{(1)} &&
\begin{tikzpicture}
\begin{scope}[start chain]
\foreach \dyi in {1,2,3,4,5,6,4,2} {
\dnode{\dyi}
}
\end{scope}
\begin{scope}[start chain=br going above]
\chainin(chain-6);
\dnodebr{3}
\end{scope}
\end{tikzpicture}
\end{align*}

\let\dlabel=\alabel

\begin{align*}
&A_2^{(2)} &&
\begin{tikzpicture}[start chain]
\dnodeanj{2}{0}
\dnodeanj{1}{1}
\path (chain-1) -- node {\QLeftarrow} (chain-2);
\end{tikzpicture}
\\
%
&A_{2l}^{(2)} (l \ge 2) &&
\begin{tikzpicture}[start chain]
\dnodeanj{2}{0}
\dnodeanj{2}{1}
\dydots
\dnodea{2}{l-1}
\dnodea{1}{l}
\path (chain-1) -- node[anchor=mid] {\(\Leftarrow\)} (chain-2);
\end{tikzpicture}
\\
%
&A_{2l-1}^{(2)} (l \ge 3) &&
\begin{tikzpicture}
\begin{scope}[start chain]
\dnodea{1}{1}
\node[chj,label={below:\dlabel{2}},label={[inner sep=1pt]above right:\mlabel{2}}] {};
\dnodea{2}{3}
\dydots
\dnodea{2}{l-1}
\dnodeanj{1}{l}
\path (chain-5) -- node[anchor=mid] {\(\Leftarrow\)} (chain-6);
\end{scope}
\begin{scope}[start chain=br going above]
\chainin(chain-2);
\node[chj,label={below left:\dlabel{0}},label={[inner sep=1pt]above right:\mlabel{1}}] {};
\end{scope}
\end{tikzpicture}
\\
%
&D_{l+1}^{(2)} (l \ge 2) &&
\begin{tikzpicture}[start chain]
\dnodea{1}{1}
\dnodeanj{1}{1}
\dydots
\dnodea{1}{l-1}
\dnodeanj{1}{l}
\path (chain-1) -- node[anchor=mid] {\(\Leftarrow\)} (chain-2);
\path (chain-4) -- node[anchor=mid] {\(\Rightarrow\)} (chain-5);
\end{tikzpicture}
\\
%
&E_6^{(2)} &&
\begin{tikzpicture}[start chain]
\dnodea{1}{0}
\dnodea{2}{1}
\dnodea{3}{2}
\dnodeanj{2}{3}
\dnodea{1}{4}
\path (chain-3) -- node[anchor=mid] {\(\Leftarrow\)} (chain-4);
\end{tikzpicture}
\end{align*}

\begin{align*}
&D_4^{(3)} &&
\begin{tikzpicture}[start chain]
\dnodea{1}{0}
\dnodea{2}{1}
\dnodeanj{1}{2}
\path (chain-2) -- node {\(\Lleftarrow\)} (chain-3);
\end{tikzpicture}
\end{align*}

\end{document}

Produces:

alt text

I'm sure that there are cleaner ways to do this, and optimisations (though, for the record, some of my experiments with the chains library didn't work correctly - indeed, I couldn't get some of the examples in the manual to compile). I tried to get it as close to the book as I could, whilst looking for a slightly more expansive and "cleaner" style (at least, as far as the preview in Google docs goes).

One of these days I'll learn what these diagrams actually mean ...

Packages loaded:

geometry: just to get the whole lot on one page
amssymb: to get the triple arrows and the left-right double arrow
mathtools: to get the mathrlap command as I preferred the labels centred on the \alpha rather than on the whole label.
tikz: to do the actual diagram
chains: to do the automatic placement of the nodes

[Tex/LaTex] Drawing tombstone diagrams

One way is to use tikz matrix,

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
\matrix (m) [matrix of nodes]
{
 C  & $\to$ &  M \\
    &  M    &    \\
  };
 \draw (m-1-1.south west) |- (m-1-3.north east) |- (m-2-2.north east) |- (m-2-2.south west) |- (m-1-1.south west);
\end{tikzpicture}
\end{document}

enter image description here

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
\matrix (m) [matrix of nodes,%nodes={minimum width=1em,minimum height=1.7em}
            ]
{
 C  & $\to$ &  M  & & C & $\to$ & M\\
    &  M    & C & $\to$ & M & M    \\
    &       &   & M  & & |[font=\tiny,yshift=4pt]|H         \\
    &       &   & |[font=\tiny]|H                \\
  };
 \draw (m-1-1.south west) |- (m-1-3.north east) |- (m-2-2.north east) |- (m-2-2.south west) |- (m-1-1.south west);
\draw (m-2-2.south east) |- (m-2-5.north east) --(m-2-5.south east) -- (m-2-5.south west) |- (m-3-4.south west) |- (m-2-2.south east);
\draw (m-2-5.north west) |- (m-1-7.north east) |- (m-2-6.north east) |- (m-2-5.south east) |- (m-2-5.north west);
\draw (m-3-4.south east) -- (m-4-4.south) -- (m-3-4.south west);
\draw (m-2-6.south east) -- (m-3-6.south) -- (m-2-6.south west);
\end{tikzpicture}
\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] How to replicate affine Dynkin diagrams in Kac’s textbook

[Tex/LaTex] Drawing tombstone diagrams

Related Question