File:Tits index Bn.svg

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Summary

Description
English: The Tits index of type Bn, created using tikz.
Source “Classification of algebraic semisimple groups”, in Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Providence, R.I.: American Mathematical Society, 1966, pages 33–62
Author David Schwein
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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Source code:

\documentclass{standalone}

\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,decorations.pathreplacing,decorations.markings}
\usetikzlibrary{fit,math,positioning,arrows.meta,shapes.geometric}
\tikzset{
n/.style={fill=black,circle, %% node
 inner sep=0pt,minimum size=4pt},
e/.style={fill=black,circle, %% ellipses
 inner sep=0pt,minimum size=2pt},
w/.style={fill=white,draw=white,circle, %% white (omitted) nodes
 inner sep=0pt,minimum size=4pt},
c/.style={ellipse,draw=black,inner sep=1pt}, %% circles 
b/.style={decoration={brace,amplitude=10pt},decorate,thick}, %% brace
a/.style={postaction={decorate,decoration={
  markings, mark=at position .5 with 
  {\arrow[black]{Straight Barb[length=\al]}}
 }}} %% mid arrow
} 

\def\v{0.5cm}  %% vertical node space
\def\h{1cm}    %% horizontal node space
\def\s{1.8pt}  %% space for weighted edges
\def\al{5pt}   %% arrow length
\def\l{2.5*\v} %% label separator

\begin{document}
\begin{tikzpicture}

%% Nodes
\node[n] (1) at (0,0) {};

\foreach \x [evaluate=\x as \y using int(\x-1)]
in {2,...,9} {
 \node[n] (\x) [right=\h of \y] {};
}

%% Edges
\foreach \x [evaluate=\x as \y using int(\x+1)]
in {1,3,4,5,7} {
 \draw (\x.center) -- (\y.center);
}

\draw[transform canvas = {yshift=\s}] (8.center) -- (9.center);
\draw[transform canvas = {yshift=-\s}] (8.center) -- (9.center);
\draw[draw=white,a] (8) -- (9);

%% Ellipses
\foreach \x [evaluate=\x as \y using int(\x+1)]
in {2,6} {
 \foreach \i in {0.25,0.5,0.75} {
  \node[e] at ($(\x)!\i!(\y)$) {};
 }
}

%% Circles
\foreach \x in {1,...,4} {
 \node[c,fit=(\x)] at (\x) {};
}

%% Braces
\draw[b] ($(4) + (0.5*\h,-\v)$) -- 
 node [label={[yshift=-\l] $r$}] {} ($(1) + (-0.5*\h,-\v)$);

\draw[b] ($(9) + (0.5*\h,-\v)$) -- 
 node [label={[yshift=-\l] $n-r$}] {} ($(5) + (-0.5*\h,-\v)$);

\end{tikzpicture}
\end{document}

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Date/TimeThumbnailDimensionsUserComment
current13:20, 26 June 2018Thumbnail for version as of 13:20, 26 June 2018364 × 63 (15 KB)David Schwein{{Information | description = The Tits index of type B<sub>''n''</sub>, created using tikz. | source = {{Citation | ref=harv | last1=Tits | first1=Jacques | author-link = Jacques Tits | title=Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) | publisher=American Mathematical Society | location=Providence, R.I. |mr=0224710 | year=1966 | chapter=Classification of algebraic semisimple groups | pages=33–62}} | date = 26 June 2018...
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