Paprika Schlesinger

Schlesinger Transformations for Bonnet Surfaces

Bonnet surfaces, i.e. surfaces in Euclidean 3-space, which admits a one-parameter family of isometries preserving the mean curvature function, can be described in terms of solutions of some special Painlev e equations. The goal of this work is to use the well-known Schlesinger transformations for solutions of Painlev e VI equations to create new Bonnet surfaces from a known one.

Hypergeometric Solution of 2 × 2q-schlesinger System Hypergeometric Solution of 2 × 2 Q-schlesinger System

Schlesinger transformations and quantum R-matrices

Schlesinger transformations are discrete monodromy preserving symmetry transformations of a meromorphic connection which shift by integers the eigenvalues of its residues. We study Schlesinger transformations for twisted slN -valued connections on the torus. A universal construction is presented which gives the elementary two-point transformations in terms of Belavin’s elliptic quantum R-matrix...

Curves , Riemann - Hilbert Problem and Schlesinger Equations

We are solving the classical Riemann-Hilbert problem of rank N > 1 on the extended complex plane punctured in 2m + 2 points, for N × N quasi-permutation monodromy matrices. Our approach is based on the finite gap integration method applied to study the Riemann-Hilbert by Kitaev and Korotkin [1], Deift, Its, Kapaev and Zhou [2] and Korotkin, [3]. This permits us to solve the Riemann-Hilbert prob...

Schlesinger transformations for algebraic Painlevé VI solutions

Various Schlesinger transformations can be combined with a direct pull-back of a hypergeometric 2×2 system to obtainRS 4 -pullback transformations to isomonodromic 2× 2 Fuchsian systems with 4 singularities. The corresponding Painlevé VI solutions are algebraic functions, possibly in different orbits under Okamoto transformations. This paper demonstrates a direct computation of Schlesinger tran...