Let $k$ be an algebraically closed field, $Q$ be a finite connected quiver and $Q'$ a subquiver of $Q$. Let $C$ be the $c$-matrix of a chamber of the scattering diagram/semi-invariant picture of $kQ$. If we remove all the walls corresponding to $c$-vectors with at least one non-zero entry in $Q_0\backslash Q'_0$ and project the diagram onto $\{x \in \mathbb{R}^{|Q_0|}:\forall i\in Q_0\backslash Q'_0\, x_i=0\}$ we can obtain a scattering diagram/semi-invariant picture of $kQ'$. In this case each chamber of the scattering diagram of $kQ$ is mapped to a chamber of the scattering diagram of $kQ'$. What are the relationships betweeen $c$-matrices corresponding to the two chambers?
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