Mirkovi\'c introduced the notion of loop Grassmannian for symmetric integer matrix κ. It is a two-step limit of the local projective space Zκα, which generalizes the usual Zastava for a simply laced group G. The usual loop Grassmannian of G is recovered when the matrix κ is the Cartan matrix of G. On the other hand, Braverman, Finkelberg, and Nakajima showed that the Compactified Coulomb branch MQα for the quiver gauge theory with no framing also generalizes the usual Zastava. We show that in the case when κ is the associated matrix of the quiver Q, these two generalizations of Zastava coincide, i.e MQα Zκ(Q)α.
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Zhijie Dong (2024) studied this question.