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Dynkin 图相关问题

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Dynkin 图相关问题

我正在努力绘制第 61 页第 8 步中的图表汉弗莱的著作《李代数和表示论导论》。由于它们不是标准的 Dynkin 图，我找不到使用包 {dynkin-diagrams} 绘制它们的方法。绘制这些图表的最简单方法是什么？感谢您的帮助。 图形

答案1

遗憾的是，这需要挖掘未记录的下一层中的隐藏特性dynkin 图包裹。 在此处输入图片描述

\documentclass{amsart}
\usepackage{dynkin-diagrams}
\makeatletter
\newcommand{\extraNode}[6]%
{%
\dynkinPlaceRootRelativeTo{#1}{#2}{#3}{#4}{#5}
\dynkinDefiniteSingleEdge{#1}{#2}
\dynkinRootMark{o}{#1}
\advance\dynkin@nodes by 1
\dynkinLabelRoot{#1}{#6} 
}%
\newcommand{\extraDotNode}[6]%
{%
\dynkinPlaceRootRelativeTo{#1}{#2}{#3}{#4}{#5}
\dynkinIndefiniteSingleEdge{#1}{#2}
\dynkinRootMark{o}{#1}
\advance\dynkin@nodes by 1
\dynkinLabelRoot{#1}{#6} 
}%
\makeatother
\tikzset{/Dynkin diagram,mark=o,edge length=.5cm}
\begin{document}
\begin{tabular}{c}
\dynkin A{}
\\
\begin{dynkinDiagram}A{ooo.o}
\dynkinLabelRoot{1}{\varepsilon_1}
\dynkinLabelRoot{2}{\varepsilon_2}
\dynkinLabelRoot{3}{\varepsilon_3}
\dynkinLabelRoot{4}{\varepsilon_p}
\dynkin[at=(root 4),arrows=false]B2
\dynkin[at=(root 2),labels={\eta_q,\eta_{q-1},\eta_2,\eta_1}]A{oo.oo}
\end{dynkinDiagram}
\\
\dynkin[arrows=false] G{2}
\\
\begin{dynkinDiagram}[labels={\varepsilon_{p-1},\psi,\zeta_{r-1},\eta_{q-1}},mark=o,edge length=.75cm]D4
\extraDotNode{5}{3}{northeast}{right}{left}{\zeta_2}
\extraDotNode{6}{4}{southeast}{right}{left}{\eta_2}
\extraDotNode{7}{1}{west}{below}{above}{\varepsilon_2}
\extraNode{8}{5}{northeast}{right}{left}{\zeta_1}
\extraNode{9}{6}{southeast}{right}{left}{\eta_1}
\extraNode{10}{7}{west}{below}{above}{\varepsilon_1}
\end{dynkinDiagram}
\end{tabular}
\end{document}

答案2

这是一种方法。

在此处输入图片描述

\documentclass{article}
\usepackage{tikz,lipsum}
\begin{document}
\lipsum[1]
\begin{center}
\begin{tikzpicture}
[edot/.style={fill=white,circle,draw,minimum size=3pt,inner sep=0,outer sep=0},xscale=1.5]  

% first line
\path 
(0,0) node{$\cdots$}
(.5,0) node[edot] (R1) {}
(1.5,0) node[edot] (R2) {}
(-.5,0) node[edot] (L1) {}
(-1.5,0) node[edot] (L2) {}
;       
\draw (L1)--(L2) (R1)--(R2);

% second line
\path 
(2,-1) node{$\cdots$}
(.5,-1) node[edot] (1R1) {} node[below=1mm]{$\eta_q$}
(1.5,-1) node[edot] (1R2) {} node[below=1mm]{$\eta_{q-1}$}
(2.5,-1) node[edot] (1R3) {} node[below=1mm]{$\eta_2$}
(3.5,-1) node[edot] (1R4) {} node[below=1mm]{$\eta_1$}
(-2,-1) node{$\cdots$}
(-.5,-1) node[edot] (1L1) {} node[below=1mm]{$\epsilon_q$}
(-1.5,-1) node[edot] (1L2) {} node[below=1mm]{$\epsilon_{q-1}$}
(-2.5,-1) node[edot] (1L3) {} node[below=1mm]{$\epsilon_2$}
(-3.5,-1) node[edot] (1L4) {} node[below=1mm]{$\epsilon_1$}
;       
\draw 
(1L1)--(1L2) (1L3)--(1L4) (1R1)--(1R2) (1R3)--(1R4)
(1L1.90)--(1R1.90) (1L1.-90)--(1R1.-90);

% third line
\path 
(.5,-2) node[edot] (2R1) {}
(-.5,-2) node[edot] (2L1) {}
;
\draw (2L1)--(2R1) (2L1.90)--(2R1.90) (2L1.-90)--(2R1.-90); 

% fourth line
\def\t{20}
\path 
(0,-4) node[edot] (3) {} node[above=1mm] {$\Psi$}
++(\t:1) node[edot] (3R1a) {} node[above=1mm]{$\zeta_{r-1}$}
++(\t:.5) node[rotate=\t]{$\cdots$}
++(\t:.5) node[edot] (3R2a) {} node[above=1mm]{$\zeta_2$}
++(\t:1) node[edot] (3R3a) {} node[above=1mm]{$\zeta_1$}
(0,-4)
++(-\t:1) node[edot] (3R1b) {} node[below=1mm]{$\eta_{q-1}$}
++(-\t:.5) node[rotate=-\t]{$\cdots$}
++(-\t:.5) node[edot] (3R2b) {} node[below=1mm]{$\eta_2$}
++(-\t:1) node[edot] (3R3b) {} node[below=1mm]{$\eta_1$}
(-1,-4) node[edot] (3L1) {} node[below=1mm]{$\epsilon_{p-1}$}
(-1.5,-4) node {$\cdots$}
(-2,-4) node[edot] (3L2) {} node[below=1mm]{$\epsilon_2$}
(-3,-4) node[edot] (3L3) {} node[below=1mm]{$\epsilon_1$}
;
\draw (3)--(3R1a) (3R2a)--(3R3a) (3)--(3R1b) (3R2b)--(3R3b)
(3)--(3L1) (3L2)--(3L3);
\end{tikzpicture}
\end{center}
\lipsum[2]
\end{document}

答案3

这为您提供了绘制图形所需的全部内容：

\documentclass[border=1cm]{standalone}

\usepackage{tikz}
\usetikzlibrary{positioning}

\begin{document}
    
    \begin{tikzpicture}
        
        \node[circle,draw,label={[yshift=-1cm]t1}] at (0,0) (t1) {};    
        \node[circle,draw,label={[yshift=-1cm]t2}] at (2,0) (t2) {};    
        \node[circle,draw,label={[yshift=-1cm]t3}] at (4,0) (t3) {};
        \node[circle,draw,label={[yshift=-1.1cm]tp}] at (6,0) (tp) {};
        \node[circle,draw,label={[yshift=-1.1cm]$n_{q}$}] at (8,0) (nq) {};
        \node[circle,draw,label={[yshift=-1.1cm]$n_{q-1}$}] at (10,0) (nq1) {};
        \node[circle,draw,label={[yshift=-1.1cm]$n_{2}$}] at (12,0) (n2) {};
        \node[circle,draw,label={[yshift=-1.1cm]$n_{3}$}] at (14,0) (n3) {};
        
        
        \draw [-] (t1) edge (t2) (t2) edge (t3) (t3) edge[line width=2pt, line cap=round, dash pattern=on 0pt off 5,shorten <=3] (tp) (tp) edge[double,double distance=4pt] (nq) (nq) edge (nq1) (nq1) edge[line width=2pt, line cap=round, dash pattern=on 0pt off 5,shorten <=3] (n2) (n2) edge (n3); 
        
        \node[circle,draw,above=of t3]  (a) {}; 
        \node[circle,draw,above=of tp]  (b) {}; 
        \node[circle,draw,above=of nq]  (c) {}; 
        \node[circle,draw,above=of nq1]  (d) {};    
        \draw [-] (a) edge (b) (b) edge[line width=2pt, line cap=round, dash pattern=on 0pt off 5,shorten <=3] (c) (c) edge (d);

    \end{tikzpicture}

    
    
\end{document}

在此处输入图片描述

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