The extended Lotka-Volterra lattice and affine Jacobi varieties of spectral curves

TL;DR

This paper links the extended Lotka-Volterra lattice to affine Jacobi varieties of spectral curves, providing a classical integrable model realization and analyzing its integrable structure and solvability.

Contribution

It introduces a new realization of affine Jacobi varieties via the extended Lotka-Volterra lattice, connecting integrable models with algebraic geometry.

Findings

The realization is given by the extended Lotka-Volterra lattice.

The integrable structure of the model is characterized.

The model's solvability is discussed through gauge equivalence classes.

Abstract

Based on the work by Smirnov and Zeitlin, we study a simple realization of the matrix construction of the affine Jacobi varieties. We find that the realization is given by a classical integrable model, the extended Lotka-Volterra lattice. We investigate the integrable structure of the representative for the gauge equivalence class of matrices, which is isomorphic to the affine Jacobi variety, and make use it to discuss the solvability of the model.