# Tau-Functions and Monodromy Symplectomorphisms

@article{Bertola2019TauFunctionsAM, title={Tau-Functions and Monodromy Symplectomorphisms}, author={Marco Bertola and Dmitry Korotkin}, journal={Communications in Mathematical Physics}, year={2019}, volume={388}, pages={245 - 290} }

We derive a new Hamiltonian formulation of Schlesinger equations in terms of the dynamical r-matrix structure. The corresponding symplectic form is shown to be the pullback, under the monodromy map, of a natural symplectic form on the extended monodromy manifold. We show that Fock–Goncharov coordinates are log-canonical for the symplectic form. Using these coordinates we define the symplectic potential on the monodromy manifold and interpret the Jimbo–Miwa–Ueno tau-function as the generating…

## 8 Citations

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### WKB expansion for a Yang–Yang generating function and the Bergman tau function

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We study symplectic properties of the monodromy map of second-order equations on a Riemann surface whose potential is meromorphic with double poles. We show that the Poisson bracket defined in terms…

### Yang-Yang generating function and Bergman tau-function

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Abstract We study symplectic properties of the monodromy map of second-order equations on a Riemann surface whose potential is meromorphic with double poles. We show that the Poisson bracket defined…

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In this paper we consider the symplectic properties of the monodromy map of second order equations on a Riemann surface whose potential is meromorphic with second order poles. We show that the…