57 citations · 117 across the 14 of their papers we have counts for
16 papers
2-dimensional finite-gap Schrödinger operator whose spectrum admits two involutions
O. K. Sheinman
Two-dimensional Schrödinger operators that are finite-gap at one energy level are introduced in 1976 by Dubrovin, Krichever and Novikov. In two subsequent works by Novikov and Vese…
Inversion of the Abel--Prym map for real curves with involutions
Oleg K. Sheinman
Riemann vanishing theorem is a main ingredient of the conventional technique related to the Jacobi inversion problem. In the case of curves with a holomorphic involution, it has be…
Inversion of the Abel--Prym map in presence of an additional involution
O. K. Sheinman
Unlike Abel map of the symmetric power of a Riemann surface onto its Jacobian, the Abel--Prym map generically can not be reversed by means of conventional technique related to the…
Hitchin systems: some recent advances
O. K. Sheinman, Bin Wang
A survey of some recent advances in parabolic Hitchin systems (parabolic Bouville--Narasimhan--Ramanan correspondence, mirror symmetry for parabolic Hitchin systems), and in exact…
Quantization of Lax integrable systems and Conformal Field Theory
Oleg K. Sheinman
We present the correspondence between Lax integrable systems with spectral parameter on a Riemann surface, and Conformal Field Theories, in quite general set-up suggested earlier b…
Hitchin systems on hyperelliptic curves
P. I. Borisova, O. K. Sheinman
We describe a class of spectral curves and find explicit formulas for Darboux coordinates for hyperelliptic Hitchin systems corresponding to classical simple Lie groups. We conside…