Canonical structure and symmetries of the Schlesinger equations
Canonical structure and symmetries of the Schlesinger equations
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DOI：
10.1007/s00220-006-0165-3
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发表时间：
2007-04-01
影响因子：
2.4
通讯作者：
Mazzocco, Marta
中科院分区：
文献类型：
--
作者：
Dubrovin, Boris;Mazzocco, Marta
Schlesinger方程S（（n，m））描述了具有n + 1个极点的m阶Fuchsian系统的单值保持变形.它们可以被认为是一族可交换的依赖于时间的Hamilton系统，其直积是m × m矩阵代数的n个副本，并配有标准的线性Poisson括号。本文给出了一般Schlesinger方程S（（n，m））对所有n，m的一种新的正则Hamilton形式，并计算了Schlesinger方程对称性在这些坐标系中的作用.
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 x 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.