Physics – Mathematical Physics
Scientific paper
2001-03-18
Physics
Mathematical Physics
To appear in "Isomonodromy deformations and applications", ed. by J.Harnad and A.Its, CRM proceedings, AMS (2001)
Scientific paper
A class of Riemann-Hilbert problems corresponding to quasi-permutation monodromy matrices is solved in terms of Szeg\"o kernel on auxiliary Riemann surfaces. The tau-function of Schlesinger system turns out to be closely related to determinant of Cauchy-Riemann operator. The link between theta-divisor and Malgrange's divisor in the theory of Schlesinger equations is established.
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