Reduction of divisors for classical superintegrable GL(3) magnetic chain

Abstract

Separated variables for a classical GL(3) magnetic chain are coordinates of a generic positive divisor D of degree n on a genus g non-hyperelliptic algebraic curve. Because n > g, this divisor D has unique representative ρ(D) in the Jacobian, which can be constructed by using dim|D| = n − g steps of Abel’s algorithm. We study the properties of the corresponding chain of divisors and prove that the classical GL(3) magnetic chain is a superintegrable system with dim|D| = 2 superintegrable Hamiltonians.