Matrix Riemann-Hilbert problems related to branched coverings of $\CP1$

dc.creatorKorotkin, D.
dc.date2001-06-13
dc.date2001-08-03
dc.date.accessioned2026-07-07T04:28:30Z
dc.date.available2026-07-07T04:28:30Z
dc.descriptionIn these notes we solve a class of Riemann-Hilbert (inverse monodromy) problems with quasi-permutation monodromy groups which correspond to non-singular branched coverings of $\CP1$. The solution is given in terms of Szegö kernel on the underlying Riemann surface. In particular, our construction provides a new class of solutions of the Schlesinger system. We present some results on explicit calculation of the corresponding tau-function, and describe divisor of zeros of the tau-function (so-called Malgrange divisor) in terms of the theta-divisor on the Jacobi manifold of the Riemann surface. We discuss the relationship of the tau-function to determinant of Laplacian operator on the Riemann surface.
dc.descriptionMinor misprints are corrected. To appear in "Operator Theory: Advances and Application", Proceedings of the Summer School on Factorization and Integrable Systems, Algarve, September 6-9, 2000. Ed by I.Gohberg, A. F. dos Santos and N.Manojlovic, Birkhauser, Boston, 2002
dc.identifierhttps://arxiv.org/abs/math-ph/0106009
dc.identifierhttp://arxiv.org/abs/math-ph/0106009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56812
dc.subjectMathematical Physics
dc.subjectPrimary 35Q15; Secondary 30F60, 32G81
dc.titleMatrix Riemann-Hilbert problems related to branched coverings of $\CP1$
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