diff --git a/main.tex b/main.tex
index 3ac0d41e8fe33d4c5892ee52cba3b72a72bab0e7..7509ef0e90ff4c96346af00cb62b8077c5090ec7 100644
--- a/main.tex
+++ b/main.tex
@@ -1,5 +1,5 @@
 \documentclass[aps, prb, twocolumn, showpacs, amsmath, amssymb, amscd,
-superscriptaddress, floatfix, longbibliography]{revtex4-2}
+superscriptaddress, floatfix, longbibliography, booktabs]{revtex4-2}
 
 \usepackage{braket}
 
@@ -15,6 +15,9 @@ superscriptaddress, floatfix, longbibliography]{revtex4-2}
 \usepackage[capitalize]{cleveref}
 \usepackage{csquotes}
 
+\usepackage{diagbox}
+\usepackage{colortbl}
+
 \usepackage{bbold}
 
 \usepackage{pifont}
@@ -44,7 +47,7 @@ superscriptaddress, floatfix, longbibliography]{revtex4-2}
     \node[shape=circle,draw,inner sep=1pt] (char) {#1};}}
 \MakeRobustCommand\circled
 
-\newcommand{\su}{SU(2)~}
+\newcommand{\su}[1]{SU(2)~}
 
 \newcommand{\bvec}[1]{\boldsymbol #1}
 \newcommand{\Ucrit}{U_\mathrm{c}}
@@ -310,10 +313,12 @@ presented in the following.
                     \Delta_{s} \Psi \\
                     \Delta_{p_x} d_x  - \Delta_{p_y} d_y
                    \end{gathered}$ \\
-    \sym A 2    & ---  & $d_z$
+    \sym A 2    & \textbf{---}  & $d_z$
                 & $\Delta_{p_y} d_x  + \Delta_{p_x} d_y$\\
-    \sym B 1 & \numberedHexagon{$\Delta_f$}{-1}{1}{-1}{1}{-1}{1} & --- & --- \\
-    \sym B 2 & --- & --- & $\Delta_{f} d_z$ \\[0.5em] \hline \\
+    \sym B 1 & \numberedHexagon{$\Delta_f$}{-1}{1}{-1}{1}{-1}{1}
+        & \textbf{---} & \textbf{---} \\
+    \sym B 2 & \textbf{---} & \textbf{---}
+        & $\Delta_{f} d_z$ \\[0.5em] \hline \\
     \sym E 1 &
     \hspace{0.15cm} % Fix spacing in the table
         $\begin{bmatrix}
@@ -333,16 +338,16 @@ presented in the following.
     \sym E 2 &
         $\left[
             \begin{aligned}
-                \numberedHexagon{$\Delta_{d_{x^2-y^2}}$}{-1}{-1}{2}{-1}{-1}{2} \\
+                \numberedHexagon{$\Delta_{d_{x^2-y^2}}$}{-1}{-1}{2\phantom{-}}{-1}{-1}{2} \\
                 \numberedHexagon{$\Delta_{d_{xy}}$}{1}{-1}{0}{1}{-1}{0}
             \end{aligned}
         \right] $
-        & ---
+        & \textbf{---}
         & \hspace{0.5cm}
         $\begin{gathered}
             \begin{bmatrix}
                 \Delta_{d_{xy}} \\
-                \Delta_{d_{x^-y^2}}
+                \Delta_{d_{x^2-y^2}}
             \end{bmatrix} \Psi \\
             \Delta_f \begin{bmatrix}
                 d_x \\
@@ -369,6 +374,51 @@ presented in the following.
     \label{tab:irrep_basis_fns}
 \end{table}
 
+\begin{table}
+    \definecolor{cell}{gray}{0.8}
+\centering
+\begin{tabular}{cccc} \toprule
+    \diagbox{$\Delta$}{$\sigma$}
+        & \sym A 1 & \sym A 2 & \sym E 1 \\ \hline
+    \sym A 1
+        & \sym A 1 : $\Delta_s \Psi$
+        & \cellcolor{cell}
+        & \cellcolor{cell} \\
+    \sym E 2
+        & \sym E 2 : $\begin{bmatrix} \Delta_{d_{xy}} \\
+            \Delta_{d_{x^2-y^2}}\end{bmatrix} \Psi$
+        & \cellcolor{cell}
+        & \cellcolor{cell} \\ \hline
+    \sym B 1
+        & \cellcolor{cell}
+        & \sym B 2 : $\Delta_f d_z $
+        & \sym E 2 : $\Delta_f \begin{bmatrix} d_x \\ d_y \end{bmatrix}$ \\
+    \sym E 1
+        & \cellcolor{cell}
+        & \sym E 1 : $\begin{bmatrix} \Delta_{p_x} \\ \Delta_{p_y} \end{bmatrix}d_z$
+        & $\begin{gathered} \sym A 1 \oplus \sym B 2 \oplus \sym E 2 : \\
+            \Delta_{p_x}d_x - \Delta_{p_y}d_y \\
+            \oplus \\
+            \Delta_{p_y}d_x + \Delta_{p_x}d_y \\
+            \oplus \\
+            \begin{bmatrix}
+                \Delta_{p_y}d_x - \Delta_{p_x}d_y \\
+            \Delta_{p_x}d_x + \Delta_{p_y}d_y \end{bmatrix}
+            \end{gathered}$
+        \\ \hline
+
+\end{tabular}
+    \caption{
+        \captiontitle{Basis functions of irreducible representations}
+        The first column lists the irreducible representation (irrep) $\gamma$.
+        The second column is the basis function in real space, for example, as
+        the bond pairing on nearest neighbour bonds. The third column is the
+        two-spin basis function, in terms of the typical superconducting psuedo-
+        vector formulation $(\Psi, \bvec d)$. The fourth column is the total
+        spatial and two-spin basis function, calculated as decribed in the text.}
+    \label{tab:irrep_combinations}
+\end{table}
+
 The divergent eigenstate will belong to one of the irreps of the point symmetry
 group of the lattice (\textit{i.e.} \sym C {6v}).
 When the Hamiltonian has an \su 2 spin symmetry, the point symmetry irreps