Toric Networks, Geometric R-Matrices and Generalized Discrete Toda Lattices

Rei Inoue, Thomas Lam, Pavlo Pylyavskyy

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We use the combinatorics of toric networks and the double affine geometric R-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 R-matrix is explicitly linearized on the Jacobian of the spectral curve. The solution to the initial value problem is constructed using Riemann theta functions.

Original languageEnglish (US)
Pages (from-to)799-855
Number of pages57
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - Nov 1 2016

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