Toric networks, geometric $R$-matrices and generalized discrete Toda lattices
Algebraic Geometry
2016-09-21 v3 Combinatorics
Exactly Solvable and Integrable Systems
Abstract
We use the combinatorics of toric networks and the double affine geometric -matrix to define a three-parameter family of generalizations of the discrete Toda lattice. We construct the integrals of motion and a spectral map for this system. The family of commuting time evolutions arising from the action of the -matrix is explicitly linearized on the Jacobian of the spectral curve. The solution to the initial value problem is constructed using Riemann theta functions.
Keywords
Cite
@article{arxiv.1504.03448,
title = {Toric networks, geometric $R$-matrices and generalized discrete Toda lattices},
author = {Rei Inoue and Thomas Lam and Pavlo Pylyavskyy},
journal= {arXiv preprint arXiv:1504.03448},
year = {2016}
}
Comments
54 pages