57 citations · 117 across the 14 of their papers we have counts for
7 papers · 1 filter
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…
Spectral curves of the hyperelliptic Hitchin systems
O. K. Sheinman
A description of the class of spectral curves, and explicit formulas for algebraic-geometric action-angle coordinates are obtained for the Hitchin systems on hyperelliptic curves,…
Some integrable systems of algebraic origin and separation of variables
O. K. Sheinman
A plane algebraic curve whose Newton polygone contains d lattice points can be given by d points it passes through. Then the coefficients of its equation Poisson commute having bee…
Some reductions of rank 2 and genera 2 and 3 Hitchin systems
Oleg K. Sheinman
Certain reductions of the rank 2, genera 2 and 3 Hitchin systems are considered, which are shown to give an integrable system of 2, resp. 3, interacting points on the line. It is s…
Lax operator algebras and integrable systems
Oleg K. Sheinman
A new class of infinite-dimensional Lie algebras given a name of Lax operator algebras, and the related unifying approach to finite-dimensional integrable systems with spectral par…