Finished the second table

main.tex

@@ -16,7 +16,6 @@ superscriptaddress, floatfix, longbibliography, booktabs]{revtex4-2}
 \usepackage{csquotes}
 
 \usepackage{diagbox}
-\usepackage{colortbl}
 
 \usepackage{bbold}
 
@@ -309,8 +308,8 @@ presented in the following.
     {$\gamma$} & Spatial Pairing & Spin Pair  \\ \hline
     \sym A 1    & \numberedHexagon{$\Delta_s$}{1}{1}{1}{1}{1}{1}
                 & $\Psi$ \\
-    \sym A 2    & ---  & $d_z$  \\
-    \sym B 1 & \numberedHexagon{$\Delta_f$}{-1}{1}{-1}{1}{-1}{1} & ---  \\
+    \sym A 2    & \textbf{---}  & $d_z$  \\
+    \sym B 1 & \numberedHexagon{$\Delta_f$}{-1}{1}{-1}{1}{-1}{1} & \textbf{---}  \\
     \sym E 1 &
     \hspace{0.2cm} % Fix spacing in the table
         $\begin{bmatrix}
@@ -326,14 +325,14 @@ presented in the following.
     \sym E 2 &
         $\begin{bmatrix}
             \hspace{0.03cm}
-            \numberedHexagon{$\Delta_{d_{x^2-y^2}}$}{-1}{-1}{2}{-1}{-1}{2}
+            \numberedHexagon{$\Delta_{d_{x^2-y^2}}$}{-1}{-1}{2{\phantom -}}{-1}{-1}{2}
             \hspace{0.03cm}
             &
             \hspace{0.03cm}
             \numberedHexagon{$\Delta_{d_{xy}}$}{1}{-1}{0}{1}{-1}{0}
             \hspace{0.03cm}
         \end{bmatrix}$
-        & --- \\[3em] \hline
+        & \textbf{---} \\[3em] \hline
 \end{tabular}
     \caption{
         \captiontitle{Basis functions of irreducible representations}
@@ -346,26 +345,25 @@ presented in the following.
 \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 2 & \sym E 1 \\ \hline \\
     \sym A 1
         & \sym A 1 : $\Delta_s \Psi$
-        & \cellcolor{cell}
-        & \cellcolor{cell} \\
+        & \textbf{---}
+        & \textbf{---} \\[1em]
     \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
+        & \textbf{---}
+        & \textbf{---} \\[1em] \hline \\
     \sym B 1
-        & \cellcolor{cell}
+        & \textbf{---}
         & \sym B 2 : $\Delta_f d_z $
-        & \sym E 2 : $\Delta_f \begin{bmatrix} d_x \\ d_y \end{bmatrix}$ \\
+        & \sym E 2 : $\Delta_f \begin{bmatrix} d_x \\ d_y \end{bmatrix}$ \\[2.5em]
     \sym E 1
-        & \cellcolor{cell}
+        & \textbf{---}
         & \sym E 1 : $\begin{bmatrix} \Delta_{p_x} \\ \Delta_{p_y} \end{bmatrix}d_z$
         & $\begin{gathered} \sym A 1 \oplus \sym B 2 \oplus \sym E 2 : \\
             \Delta_{p_x}d_x - \Delta_{p_y}d_y \\
@@ -376,17 +374,14 @@ presented in the following.
                 \Delta_{p_y}d_x - \Delta_{p_x}d_y \\
             \Delta_{p_x}d_x + \Delta_{p_y}d_y \end{bmatrix}
             \end{gathered}$
-        \\ \hline
+        \\[5em] \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.}
+        \captiontitle{Allowed combinations of irreps}
+        We show the allowed combinations of spin ($\sigma$) and spatial
+        ($\Delta$) irreps, giving the resulting total irrep as well as the
+        corresponding basis function.}
     \label{tab:irrep_combinations}
 \end{table}
 
@@ -414,7 +409,7 @@ spin-pair and spatial pairing irreps.
 We retain only the products that yield physical states, \textit{i.e.} those
 which are antisymmetric under exchange of all quantum indices (\sym E 2 $\otimes$
 \sym E 1 would yield spatially even spin-triplet pairing and is discarded).
-Except for the case $\sym E 1 \otimes \sym E 1$, either the spacial or the
+Except for the case $\sym E 1 \otimes \sym E 1$, either the spatial or the
 spin-pair space is one-dimensional.
 In those cases, multiplication of the irreps' group characters yields the
 total state's characters, and thus the total irrep.
@@ -643,8 +638,9 @@ constructed from the two generators, which are one of the $C_6$ rotations:
     \begin{pmatrix}
         \sqrt{3} - i & 0 \\
         0 & \sqrt{3} + i
-    \end{pmatrix} ,
+    \end{pmatrix}\, ,
 \end{equation}
+
 where $\hat\sigma_z$ is the third Pauli matrix, as well as a reflection $m_y$,
 which we will take to be the mirror w.r.t. the $y$-axis:
 \begin{equation}