% This is a TikZ implementation of the root system for the class G2.
% The numbering follows the one used by LiE (http://http://wwwmathlabo.univ-poitiers.fr/~maavl/LiE/),
% and the short root is denoted by \alpha and the long root by \beta
% The highest root is denoted by \gamma_{\star}.
%
%  You'll need to load the following packages
%% \usepackage{tikz}
%% \usetikzlibrary{calc}   % this is needed in order to be able to do coordinate calculations
%% \usetikzlibrary{topaths}
%% \usetikzlibrary{decorations}
%% \usetikzlibrary{decorations.pathmorphing}
%
% Feel free to use it whereever you like, but please leave my name in the drawing.
% 
% 08/04/2015, P. Meessen 
\begin{figure}[t]
  \centering
  \begin{tikzpicture}
    %%%%%%%%    08/04/2015, P. Meessen 
   [scale=.8,
     kutje/.style={circle,draw=black,fill=white, thick, inner sep=0pt, minimum size=7mm}
   ]
     %% draw the background coordinate-grid
    % \draw[step=.5cm,color=gray] (-6,-6) grid (6,6);
    % \draw[color=blue] (-6,0) node[anchor= east] {x=-6} -- (6,0) node[anchor= east] {x=6};
    % \draw[color=blue] (0,-6) node {y=-6} -- (0,6) node {y=6};
    %%%% Basic Triangle
    %% (a) is the origin
    \coordinate (a) at (0,0);
    %% the vertices, b1,..., b5 defined by rotations on b0
    \coordinate (b0) at (3,0);
    \coordinate (b1) at ($ (a)! 1! 60:(b0) $);
    \coordinate (b2) at ($ (a)! 1! 120:(b0) $);
    \coordinate (b3) at ($ (a)! 1! 180:(b0) $);
    \coordinate (b4) at ($ (a)! 1! 240:(b0) $);
    \coordinate (b5) at ($ (a)! 1! -60:(b0) $);
    \coordinate (c0) at ($ (a)! 1.7! 150:(b0) $);
    \coordinate (c1) at ($ (a)! 1.7! 30:(b0) $);
    \coordinate (c2) at ($ (a)! 1.7! 90:(b0) $);
    \coordinate (c3) at ($ (a)! 1.7! -150:(b0) $);
    \coordinate (c4) at ($ (a)! 1.7! -30:(b0) $);
    \coordinate (c5) at ($ (a)! 1.7! -90:(b0) $);
    %% draw the triangle 
    \draw[color=black, line width=1pt,->] (a) -- (b0) node[color=black, right] {$\alpha$};
    \draw[color=black, line width=1pt,->] (a) -- (b1);
    \draw[color=black, line width=1pt,->] (a) -- (b2);
    \draw[color=black, line width=1pt,->] (a) -- (b3);
    \draw[color=black, line width=1pt,->] (a) -- (b4);
    \draw[color=black, line width=1pt,->] (a) -- (b5);
    \draw[color=black, line width=1pt,->] (a) -- (c0) node[color=black, left] {$\beta$};
    \draw[color=black, line width=1pt,->] (a) -- (c1);
    \draw[color=black, line width=1pt,->] (a) -- (c2) node[color=black, right] {$\gamma_{\star}$};
    \draw[color=black, line width=1pt,->] (a) -- (c3);
    \draw[color=black, line width=1pt,->] (a) -- (c4);
    \draw[color=black, line width=1pt,->] (a) -- (c5);
    %% draw the atoms
    %\node at (b0) [kutje] {$A_{0}$};
  %%%%% end of the drawing
\end{tikzpicture}
  \caption{
     The root diagram of $\mathfrak{g}_{2}$. The short basis-root is denoted by $\alpha$ and has length $\langle\alpha |\alpha\rangle =2$, and the 
     long basis root is denoted by $\beta$ and has length $\langle\beta |\beta\rangle =6$; the angle between the roots $\alpha$ and $\beta$ is 
     $5\pi /6=150^{\degree}$.
     The highest root is denoted by $\gamma_{\star}=2\beta\ +\ 3\gamma$. In {\tt LiE} the root $\alpha$ is denoted by $1$ and $\beta$ by $2$.
  }
  \label{fig:G2Roots}
\end{figure}