Loop Grassmannian of quivers and Compactified Coulomb branch of quiver gauge theory with no framing

Mirković introduced the notion of loop Grassmannian for symmetric integer matrix $\kappa$. It is a two-step limit of the local projective space $Z_{\kappa }^{\alpha }$, which generalizes the usual Zastava for a simply laced group $G$. The usual loop Grassmannian of $G$ is recovered when the matrix $\kappa$ is the Cartan matrix of $G$. On the other hand, Braverman, Finkelberg, and Nakajima showed that the Compactified Coulomb branch ${\mathbf{M}}_Q^{\alpha }$ for the quiver gauge theory with no framing also generalizes the usual Zastava. We show that in the case when $\kappa$ is the associated matrix of the quiver $Q$, these two generalizations of Zastava coincide, i.e ${\mathbf{M}}_Q^{\alpha }\cong Z_{\kappa (Q)}^{\alpha }$.