Como fazer setas entre as tabelas e fazer letras pequenas para o conteúdo

Question

Tenho duas dúvidas: Primeiramente: Como abrir espaço entre duas tabelas e desenhar setas para mostrar a correspondência entre as linhas (quero dizer, a primeira linha da tabela da esquerda corresponde à primeira linha da tabela da direita). Segundo: como fazer letras pequenas na terceira linha de cada tabela. Postei minha tentativa e agora está funcionando:

\documentclass {article}
\usepackage{array}
\usepackage{multirow}
\usepackage{amsmath,amsfonts,amssymb,array,subfigure,graphics,epsfig}
\usepackage{mathrsfs}
\usepackage{extarrows}
\usepackage{caption}
\usepackage{float}
\usepackage{multirow}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{blindtext}
\usepackage{graphicx}
\usepackage{flexisym}
\newcommand{\vect}[1]{\boldsymbol{#1}}
\usepackage[mathscr]{eucal}
\usepackage{color,soul}
\usepackage{enumitem}
\usepackage{cancel}
\usepackage{nicefrac}
\usepackage{flexisym}
\usepackage{ytableau}
\usepackage{youngtab}
\usepackage{mathtools}


\begin{document}%
\small
\begin{tabular}{cc}%
\begin{tabular}[t]{| m{3em} | m{5cm}|}
\hline
 \multicolumn{2}{|c|}{Irreducibles for the maximal subgroups $G_{e}$} \\
 \hline
\multicolumn{2}{|c|}{$S^{(0)}= 0 \ \ \mbox{[zero vector]}$} \\
\hline
\multicolumn{2}{|c|}{$S^{(2,1)}\ $} \\
\hline
\multicolumn{2}{|c|}{$
     S^{(2,1)}= \Bigg\{c_{1} e_{_{\ytableausetup
     {mathmode, boxsize=1em, centertableaux}\begin{ytableau}
 \tiny{1} &  3 \\ 2
\end{ytableau}}}+c_{2}e_{_{\ytableausetup
     {mathmode, boxsize=1em, centertableaux}\begin{ytableau}
 \tiny{1} &  2 \\ 3
     \end{ytableau}}}
\Bigg \} 
   $} \\
\hline
\end{tabular} &
\begin{tabular}[t]{| m{3em} | m{5cm}|}
\hline
 \multicolumn{2}{|c|}{Irreducibles for the symmetric inverse monoid $I_{4}$} \\
\hline
\multicolumn{2}{|c|}{$R^{(0)}= 0 \ \ \mbox{zero vector.}$} \\
\hline
\multicolumn{2}{|c|}{$R^{(2,1)}$} \\
\hline
\multicolumn{2}{|c|}{$
   R^{(2,1)}= \Bigg \{
   c_{1}e_{_{\ytableausetup
     {, smalltableaux, centertableaux}\begin{ytableau}
 1 & 3 \\ 2
\end{ytableau}}}+c_{2}e_{_{\ytableausetup
     {, smalltableaux, centertableaux}\begin{ytableau}
 1 & 4 \\ 2 
\end{ytableau}}}+c_{3}e_{_{\ytableausetup
     {, smalltableaux, centertableaux}\begin{ytableau}
 1 & 2 \\ 3   
\end{ytableau}}}+c_{4}e_{_{\ytableausetup
     {, smalltableaux, centertableaux}\begin{ytableau}
 1 & 4 \\ 3  
\end{ytableau}}}+c_{5}e_{_{\ytableausetup
     {, smalltableaux, centertableaux}\begin{ytableau}
 2 & 4 \\ 3  
\end{ytableau}}}+c_{6}e_{_{\ytableausetup
     {, smalltableaux, centertableaux}\begin{ytableau}
 1 & 2 \\ 4  
\end{ytableau}}}+c_{7}e_{_{\ytableausetup
     {, smalltableaux, centertableaux}\begin{ytableau}
 1 & 3 \\ 4  
\end{ytableau}}}+c_{8}e_{_{\ytableausetup
     {, smalltableaux, centertableaux}\begin{ytableau}
 2 & 3 \\ 4  
\end{ytableau}}}
    \Bigg \} $} \\
\hline
\end{tabular} \tabularnewline
\end{tabular}

\end{document}

Answer 1

\documentclass {article}
\usepackage{mathtools}

\newcommand\tristrut{\rule[-1pt]{0pt}{5pt}}
\newcommand\tri[3]%
  {\raisebox{-1ex}%
    {\tiny\tabcolsep=1pt\renewcommand\arraystretch{0}%
     \begin{tabular}{|c|c|}
     \hline
     \tristrut#1 & #2 \\
     \hline
     \tristrut#3 \\
     \cline{1-1}
     \end{tabular}%
    }%
  }

\begin{document}%
\[\renewcommand\arraystretch{1.5}%
  \begin{array}{@{}c@{\quad\Longrightarrow\quad}c@{}}
    \renewcommand\arraystretch{1}%
    \begin{tabular}{@{}c@{}}
      Irreducibles for the\\
      maximal subgroups $G_{e}$
    \end{tabular}
  & \begin{tabular}{@{}c@{}}
      Irreducibles for the\\
      symmetric inverse monoid $I_{4}$
    \end{tabular}
  \\
    S^{(0)}= 0\quad\text{zero vector}
  & R^{(0)}= 0\quad\text{zero vector}
  \\
    S^{(2,1)}
  & R^{(2,1)}
  \\
    S^{(2,1)}= \big\{c_1 e_{\tri132} +c_2e_{\tri123} \big\}
  & \begin{aligned}[t]
      R^{(2,1)}= \big \{
      & c_1e_{\tri132} + c_2e_{\tri142} + c_3e_{\tri123} + c_4e_{\tri143} + {}\\
      & c_5e_{\tri243} + c_6e_{\tri124} + c_7e_{\tri134} + c_8e_{\tri234}\quad \big \}
     \end{aligned}
  \end{array}
\]
\end{document}