2001/06/13 by D. Korotkin, Korotkin, D.
Mathematics · Physics and Astronomy · #32G81 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 35Q15 #Secondary 30F60 #math-ph #math.MP #msc:30F60 #msc:32G81 #msc:35Q15
paper · pdf · doi:10.48550/arxiv.math-ph/0106009
Minor 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
openalex publication_date 2001/06/13 · arxiv created 2001/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 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.