Demazure weaves for reduced plabic graphs (with a proof that Muller-Speyer twist is Donaldson-Thomas)
arXiv (Cornell University)(2023)
摘要
First, this article develops the theory of weaves and their cluster
structures for the affine cones of positroid varieties. In particular, we
explain how to construct a weave from a reduced plabic graph, show it is
Demazure, compare their associated cluster structures, and prove that the
conjugate surface of the graph is Hamiltonian isotopic to the Lagrangian
filling associated to the weave. The T-duality map for plabic graphs has a
surprising key role in the construction of these weaves. Second, we use the
above established bridge between weaves and reduced plabic graphs to show that
the Muller-Speyer twist map on positroid varieties is the Donaldson-Thomas
transformation. This latter statement implies that the Muller-Speyer twist is a
quasi-cluster automorphism. An additional corollary of our results is that
target labeled seeds and the source labeled seeds are related by a
quasi-cluster transformation.
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关键词
reduced plabic graphs,muller-speyer,donaldson-thomas
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