Isomonodromic deformations and Hurwitz spaces
نویسنده
چکیده
Here we solve N × N Riemann-Hilbert (inverse monodromy) problems with all monodromy matrices having the structure of matrices of quasi-permutation (i.e. matrices which have only one non-zero element in each column and each row). Such RiemannHilbert problem may be associated to arbitrary Hurwitz space of algebraic curves L of genus g realized as N -sheeted covering over CP1, and allowes solution in terms of Szegö kernel on L. If we denote coordinate on CP1 by λ and projections of the branch points to complex plane by λ1, . . . , λn then the solution of inverse monodromy problem of that type has the following form:
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