Some reductions of rank 2 and genera 2 and 3 Hitchin systems

TL;DR

This paper explores specific reductions of rank 2, genus 2 and 3 Hitchin systems, demonstrating their connection to universal integrable systems and using computational methods to verify admissibility.

Contribution

It introduces new reductions of Hitchin systems linked to universal integrable systems and employs computer techniques to prove their admissibility.

Findings

Reduced systems describe interacting points on a line

Connections established with Lagrange interpolation polynomial

Computer verification of reduction admissibility

Abstract

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 shown that the reduced systems are particular cases of a certain universal integrable system related to the Lagrange interpolation polynomial. Admissibility of the reduction is proved using computer technique. The corresponding codes are given in the text.