An explicit inverse matrix A_{u,beta} is constructed for braid varieties; its frozen columns generate the cluster automorphism group action, and the matrix is proven invertible with determinant plus or minus one.
Demazure weaves from 3D plabic graph, In preparation
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Cluster automorphism group of braid varieties
An explicit inverse matrix A_{u,beta} is constructed for braid varieties; its frozen columns generate the cluster automorphism group action, and the matrix is proven invertible with determinant plus or minus one.