diff --git a/main.tex b/main.tex
index 78718754ea2f13b71b37d17717893de25c266ff7..f377c3bff9356c98c4a93cd56e78507e11141aa6 100644
--- a/main.tex
+++ b/main.tex
@@ -44,7 +44,7 @@ superscriptaddress, floatfix, longbibliography]{revtex4-2}
     \node[shape=circle,draw,inner sep=1pt] (char) {#1};}}
 \MakeRobustCommand\circled
 
-\newcommand{\su}{SU}
+\newcommand{\su}{SU(2)~}
 
 \newcommand{\bvec}[1]{\boldsymbol #1}
 \newcommand{\Ucrit}{U_\mathrm{c}}
@@ -252,7 +252,7 @@ Thorough derivations of the FRG equations can be found in
 Refs.\,\onlinecite{metzner2012,dupuis2021,platt2013,beyer2022a}
 among others, here we only give the briefest overview of our chosen
 approximations:
-The diagrammatic representation of our single-loop, non-$SU(2)$ flow-equation
+The diagrammatic representation of our single-loop, non-\su flow-equation
 is given in \cref{fig:diags}.
 During the calculation we neglect higher loop orders, the flow equations for
 the self-energy $\frac{\dd}{\dd\Lambda}\Gamma^{(2)}$ as well as the
@@ -289,7 +289,11 @@ we determine.
 The second important property is the state's total irreducible representation
 (irrep), which must be equal in both spin spaces\,\cite{sigrist1987}.
 This can be obtained from the simulated momentum's irrep in conjunction with
-the respective spin's irrep.
+the respective spin's irrep, in accordance with the eigenstate's product
+decomposition
+\begin{equation}
+    v = \Psi \otimes \Delta_{\Psi}(\bvec k) + \bvec d \otimes \Delta_{\bvec d}(\bvec k)
+\end{equation}
 A careful symmetry analysis in conjunction with the possible combinations is
 presented in the following.