arXiv math/06103272006-10-10math.DGmath.CA

On the Reductions and Classical Solutions of the Schlesinger equations

B. Dubrovin, M. Mazzocco

备注：: 32 pages. To the memory of our friend Andrei Bolibruch

英文摘要：

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 address the problem of reduction of particular solutions of ``more complicated'' Schlesinger equations $S_{(n,m)}$ to ``simpler'' $S_{(n',m')}$ having $n'< n$ or $m' < m$.

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