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- W4226133602 abstract "Abstract Using Fock–Goncharov higher Teichmüller space variables we derive log-canonical coordinate representation for entries of general symplectic leaves of the $mathcal A_n$ groupoid of upper-triangular matrices and, in a more general setting, of higher-dimensional symplectic leaves for algebras governed by the reflection equation with the trigonometric $R$-matrix. The obtained results are in a perfect agreement with the previously obtained Poisson and quantum representations of groupoid variables for $mathcal A_3$ and $mathcal A_4$ in terms of geodesic functions for Riemann surfaces with holes. We realize braid-group transformations for $mathcal A_n$ via sequences of cluster mutations in the special $mathcal A_n$-quiver. We prove the groupoid relations for normalized quantum transport matrices and, as a byproduct, obtain the Goldman bracket in the semiclassical limit. We prove the quantum algebraic relations of transport matrices for arbitrary (cyclic or acyclic) directed planar network.Dedicated to the memory of a great mathematician and person, Boris Dubrovin." @default.
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- W4226133602 date "2022-05-18" @default.
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- W4226133602 title "OUP accepted manuscript" @default.
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- W4226133602 doi "https://doi.org/10.1093/imrn/rnac101" @default.
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