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Braid variety cluster structures, I: 3D plabic graphs

Published 10 Oct 2022 in math.CO, math.AG, math.RA, and math.RT | (2210.04778v3)

Abstract: We introduce $3$-dimensional generalizations of Postnikov's plabic graphs and use them to establish cluster structures for type $A$ braid varieties. Our results include known cluster structures on open positroid varieties and double Bruhat cells, and establish new cluster structures for type $A$ open Richardson varieties.

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