TY - JOUR T1 - On the reductions and classical solutions of the Schlesinger equations JF - Differential equations and quantum groups, IRMA Lect. Math. Theor. Phys. 9 (2007) 157-187 Y1 - 2007 A1 - Boris Dubrovin A1 - Marta Mazzocco AB - The Schlesinger equations S(n,m) describe monodromy preserving\\r\\ndeformations of order m Fuchsian systems with n+1 poles. They\\r\\ncan be considered as a family of commuting time-dependent Hamiltonian\\r\\nsystems on the direct product of n copies of m×m matrix algebras\\r\\nequipped with the standard linear Poisson bracket. In this paper we address\\r\\nthe problem of reduction of particular solutions of “more complicated”\\r\\nSchlesinger equations S(n,m) to “simpler” S(n′,m′) having n′ < n\\r\\nor m′ < m. PB - SISSA UR - http://hdl.handle.net/1963/6472 U1 - 6418 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER -