[Tex/LaTex] How to draw these Young tableaux type diagrams

diagramsytableau

I am writing an essay on a certain type of representation theory and I would be very grateful if someone can tell me how I can make these diagrams in LaTeX. Any and all help is much appreciated!

enter image description here
enter image description here
enter image description here
enter image description here
enter image description here
enter image description here
enter image description here

Best Answer

I didn't know about the package and wanted to learn something new. (And I wish the package already existed earlier.)

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\newcommand{\tikznode}[3][inner sep=0pt]{\tikz[remember
picture,baseline=(#2.base)]{\node(#2)[#1]{$#3$};}}

\usepackage{ytableau}

\begin{document}
\ytableausetup{centertableaux}
\begin{ytableau}
       \none[2] &  &  & \none \\
  \none[1]  &  &  &  \\
  \none & \none[1] & \none[2] & \none[3]
\end{ytableau}

\begin{ytableau}
       1. & \none & \none & 2. \\
  \none  & 3. & 4. & 5.
\end{ytableau}


\ydiagram{2,1+1}\ and \ydiagram{0+1,2,0+1}

\ydiagram{2,1+1,2+1,2+2,2+1}

\[ U:=F\cup G'\simeq\vcenter{\hbox{\begin{tikzpicture}
\draw (0,0) -- ++(0,2) --++(-2,0) -- ++(0,-1) --++(1,0) --++(0,-1) -- cycle
node[above left=0pt,draw]{$x$} node[above left=1cm]{$F$};
\draw (0,0) -- ++(0,-2) --++(2,0) -- ++(0,0.5) --++(-0.5,0) --++(0,1.5) -- cycle
node[below right=0pt,draw]{$y$} node[below right=1cm]{$G'$};
\end{tikzpicture}}}\]
% it is straightforward to split the tikzpicture into two

\[
\begin{ytableau}
       ~ & \none & \none & \none & \none\\
       ~ & \none & \none & \none & \none\\
       \vdots & \none & \none & \none & \none\\
       x & \none & \none & \none & \none\\
       \none &  & \cdots & 
\end{ytableau}
~+~
\begin{ytableau}
       ~ & \none & \none & \none & \none\\
       ~ & \none & \none & \none & \none\\
       \vdots & \none & \none & \none & \none\\
       x &  &  & \cdots & 
\end{ytableau}
~=~
\begin{ytableau}
       ~ & \none & \none & \none & \none\\
       ~ & \none & \none & \none & \none\\
       \vdots & \none & \none & \none & \none\\
       x & \none & \none & \none & \none\\
       ~ &  &  & \cdots & 
\end{ytableau}
\]

\[
\begin{ytableau}
       \tikznode{a1}{~} & \cdots & \tikznode{a2}{~}& \none & \none & \none\\
       \none & \none & \none & \tikznode{a3}{~} & \cdots & \tikznode{a4}{~}
\end{ytableau}
\]
\tikz[overlay,remember picture]{%
\draw[decorate,decoration={brace},thick] ([yshift=-2mm,xshift=2mm]a2.south east) -- 
([yshift=-2mm,xshift=-2mm]a1.south west) node[midway,below]{$q_1$};
\draw[decorate,decoration={brace},thick] ([yshift=-2mm,xshift=2mm]a4.south east) -- 
([yshift=-2mm,xshift=-2mm]a3.south west) node[midway,below]{$q_2$};
}
% this should allow you to draw the full thing

\end{document}

enter image description here

Related Question