diff --git a/main.tex b/main.tex
index e73065d2e8a7ef4efc795d922abee8a002f4b04d..78718754ea2f13b71b37d17717893de25c266ff7 100644
--- a/main.tex
+++ b/main.tex
@@ -271,9 +271,7 @@ capture spin-momentum locking. For a more complete technical discussion of the
 approximations and numerical implementations we refer the reader to
 Ref.\,\onlinecite{beyer2022a}.
 
-\subsection{Analysis of Results}
-
-\subsubsection{Particle-particle instabilities}
+\subsection{Singlet-Triplet decomposition}
 To determine the nature of particle-particle instabilities we calculate the
 P-channel truncated unity susceptibility as previously described in
 Ref.~\cite{beyer2022a,klebl2022a}.
@@ -295,9 +293,8 @@ the respective spin's irrep.
 A careful symmetry analysis in conjunction with the possible combinations is
 presented in the following.
 
-\todo{Helical state as limit}
 
-\subsubsection{Irreducible Representations under Rashba-SOC}
+\subsection{Irreducible Representations under Rashba-SOC}
 
 \begin{table}
 \centering
@@ -312,20 +309,23 @@ presented in the following.
     \sym A 2    & ---  & $d_z$
                 & $\Delta_{p_y} d_x  + \Delta_{p_x} d_y$\\
     \sym B 1 & \numberedHexagon{$\Delta_f$}{-1}{1}{-1}{1}{-1}{1} & --- & --- \\
-    \sym B 2 & --- & --- & $\Delta_{f} d_z$ \\ \hline
+    \sym B 2 & --- & --- & $\Delta_{f} d_z$ \\[0.5em] \hline \\
     \sym E 1 &
+    \hspace{0.15cm} % Fix spacing in the table
         $\begin{bmatrix}
             \numberedHexagon{$\Delta_{p_x}$}{1}{-1}{-2}{-1}{1}{2} \\
             \numberedHexagon{$\Delta_{p_y}$}{1}{1}{0}{-1}{-1}{0}
         \end{bmatrix} $
-        & $\begin{bmatrix}
+    \hspace{0.15cm} % Fix spacing in the table
+        &
+        $\begin{bmatrix}
             d_x \\
             d_y
         \end{bmatrix}$
         & $\begin{bmatrix}
             \Delta_{p_x} \\
             \Delta_{p_y}
-        \end{bmatrix} d_z $  \\[3em]
+        \end{bmatrix} d_z $  \\[6em]
     \sym E 2 &
         $\left[
             \begin{aligned}
@@ -352,7 +352,7 @@ presented in the following.
         \end{bmatrix}
         \end{gathered}$
         \hspace{0.5cm}
-            \\[3em] \hline
+            \\[6em] \hline
 \end{tabular}
     \caption{
         \captiontitle{Basis functions of irreducible representations}
@@ -362,59 +362,50 @@ presented in the following.
         two-spin basis function, in terms of the typical superconducting psuedo-
         vector formulation $d$. The fourth column is the total
         spatial and two-spin basis function, calculated as decribed in the text.}
-    \label{tab:irrep-basis-fns}
+    \label{tab:irrep_basis_fns}
 \end{table}
 
-As mentioned above, when analysing the results of the FRG flow, we classify the
-divergent superconducting instability by its symmetry
-behaviour\,\cite{sigrist1987}.  \todo{better citation for symmetry analysis in
-FRG?} The divergent eigenstate will belong to one of the irreducible
-representations, or irreps, of the point symmetry group of the lattice.  This
-is easiest done in systems where the $SU(2)$ symmetry of the spins remains
-preserved, as we may then ignore the symmetric spin degree of freedom of our
-eigenstate, and the irrep of the entire state can be fully understood by
-symmetry of the spatial pairing, \textit{i.e.} by analysing the symmetry of the
-real space bond order or the momentum space pairing.  For example, the
-triangular lattice has a point symmetry group $C_{6v}$, and the irrep breakdown
-of superconducting states can be classified by matching the spatial pairing
-with one of the spatial irrep basis functions. A breakdown of these functions
-shown in the second coloumn of Table \ref{tab:irrep-basis-fns}.
-
-When the $SU(2)$ symmetry of the spins is broken by the introduction of
-spin-oribtal coupling, the transformation behaviour of
-the spins under symmetry group actions can no longer be ignored\,\cite{kaba2019}.
-Instead, we aim to build an irrep basis by understanding the symmetry of the
-spatial component of our state in combination with the two spins of our
-superconducting states, \textit{i.e.} how the whole state transforms under
-group symmetry actions.
-
-To construct the irrep basis functions for the overall states, we first consider
-how just the two spins transform under the point symmetry group $C_{6v}$. The details on how
-the two-spin irrep basis functions were calculated can be found in
-Appendix\,\ref{app:spin-irreps}, and the functions themselves are listed in the
-third column of Table \ref{tab:irrep-basis-fns} .
-
-The overall basis function irreps can then be constructed from the tensor product of
-the two-spin and spatial irreps. We only take those products which give us physical
-states, \textit{i.e.} those which are antisymmetric under exchange of all quantum indices.
-For example, $E_2 \otimes E_1$ would describe spatially even ($d$-wave)
-spin-triplet states, which are not physical.
-For all but one of the possible physical products, at least one of the two
-irreps going into the tensor product is one-dimensional,
-meaning we can simply multiply the group characters of the two intial irreps, and
-the resulting set of characters will tell us what the resulting irrep is.
-
-The one special case, $\sym E 1 \otimes \sym E 1$, requires a further decomposition.
+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 state is a spin singlet or \su, this can be identified by matching the
+spacial symmetry behavior with one of the spacial irrep basis functions shown
+in \cref{tab:irrep_basis_fns}, second column.
+
+If the \su symmetry is broken by the introduction of SOC, the transformation
+behaviour of the spins under symmetry group operations must be
+considered\,\cite{kaba2019}.
+Here, the total irrep can be understood only as a combination of
+the spatial symmetry and the symmetry behavior of the two spins, \textit{i.e.}
+the total symmetry transformation behavior.
+To construct appropriate basis functions, we first consider the transformation
+behavior of a pair of spins under \sym C {6v}. The details of this calculation
+can be found in \cref{app:spin_irreps}, the resulting functions are given in
+\cref{tab:irrep_basis_fns}, third column.
+
+The total irreps is constructed as the tensor product of the spin-pair and
+spatial irreps.
+We retain only the products that yield physical states, \textit{i.e.} those
+which are antisymmetric under exchange of all quantum indices ($E_2 \otimes
+E_1$ would yield spacially even spin-triplet pairing and is discarded).
+Except for the case $\sym E 1 \otimes \sym E 1$, \todo{what about $E2
+\otimes E2$?} either the spacial 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.
+
+The $\sym E 1 \otimes \sym E 1$ case requires a further decomposition.
 This can be done by either forming irrep projection operators for the total
-representation, as described in Appendix \ref{app:spin-irreps}, or by a group
-theoretic calculation exploiting the orthogonality of the group characters \todo{source?}.
-The results is the following decomponsition:
+representation, as described in \cref{app:spin_irreps} \todo{Is this actually
+in here?}, or by a group theory calculation exploiting the orthogonality of
+the group characters \todo{source?}.
+Either results in:
 \begin{equation}
     \sym E 1 \otimes \sym E 1 = \sym A 1 \oplus \sym B 2 \oplus \sym E 2 \, .
 \end{equation}
-All of the basis functions of the combined spin-momentum system are given in
-fourth column of Table \ref{tab:irrep-basis-fns}.
+We show all possible basis functions for each irrep in
+\cref{tab:irrep_basis_fns}, fourth column.
 
+\subsection{Limit of strong spin-orbit coupling}
+\todo{Helical state as limit}
 
 
 \section{Results for the nearest-neighbor model}
@@ -613,7 +604,7 @@ effect of the Rashba SOC.
 \appendix
 
 \section{Irreducible representation basis functions in the spin representation}
-\label{app:spin-irreps}
+\label{app:spin_irreps}
 
 To get the irreducible representations of the two spins, we begin by
 constructing the symmetry group representation of for a single spin, which we
@@ -651,7 +642,7 @@ where $\chi(g)$ is the character of group element $g$, $|G|$ is the order of the
 group (which is 12 for $C_{6v}$), and $d_\mu$ is the dimension of the irrep $\mu$.
 The basis functions of the irrep are then the non-zero eigenvectors of the projection
 operators. For the two spins, the calculated basis functions are
-listed in Table\,\ref{tab:spin-irreps}.
+listed in Table\,\ref{tab:irrep_basis_fns}.
 
 \bibliographystyle{apsrev4-2}
 \bibliography{references}