Canonical structure and symmetries of the Schlesinger equations

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The Schlesinger equations $S_{(n,m)}$ describe monodromy preserving deformations of order $m$ Fuchsian systems with $n+1$ poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of $n$ copies of $m\times m$ matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation of the general Schlesinger equations $S_{(n,m)}$ for all $n$, $m$ and we compute the action of the symmetries of the Schlesinger equations in these coordinates.
92 pages, no figures. Theorem 1.2 corrected, other misprints removed. To appear on Comm. Math. Phys

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Differential Geometry, Classical Analysis and ODEs, Exactly Solvable and Integrable Systems, 32G34 (Primary); 34M55, 53D30 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/121435

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0311261
 http://arxiv.org/abs/math/0311261

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arXiv