# How can I draw these Young tableaux type diagrams?

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!

• Welcome to TeX.se. You've tagged this question ytableau which make sense because there is such a package to draw these types of diagrams. So perhaps you could post an example document using that package to show what you're having trouble with. Also the bottom picture is quite different from the top ones and so might warrant a separate question. But again, show us what you have tried. – Alan Munn Apr 30 '18 at 19:36
• Hey Alan, thanks for pointing that out! I did not realize that ytableau is a package. I will look into its documentation asap and see what problems I run into! – Character Theory Nonsense Apr 30 '18 at 20:00
• Perhaps related: tex.stackexchange.com/questions/417194/… – Steven B. Segletes May 1 '18 at 0:24

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}