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Categorified Cluster Structures on Coulomb Branches of Certain Star-Shaped Quivers
We construct quantum cluster structures on a family of quantized $K$-theoretic Coulomb branches and prove that the associated loop-graded Koszul-perverse hearts give monoidal categorifications of these algebras. For each $r\geq1$, the gauge group is the image of $GL_2\times(\mathbb{C}^*)^r$ in $GL((
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