Tau-Functions and Monodromy Symplectomorphisms

Tau-Functions and Monodromy Symplectomorphisms

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 coordin...

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Veröffentlicht in:Communications in mathematical physics 2021-11, Vol.388 (1), p.245-290
Hauptverfasser: Bertola, M., Korotkin, D.
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Sprache:eng
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Classical and Quantum Gravitation
Complex Systems
Manifolds
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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description 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 function of the monodromy map. This, in particular, solves a recent conjecture by A. Its, O. Lisovyy and A. Prokhorov.
doi_str_mv 10.1007/s00220-021-04224-6
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subjects Classical and Quantum Gravitation
Complex Systems
Manifolds
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
title Tau-Functions and Monodromy Symplectomorphisms
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