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

Rei Inoue; Thomas Lam; Pavlo Pylyavskyy

doi:10.1007/s00220-016-2739-z

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

Rei Inoue, Thomas Lam, Pavlo Pylyavskyy

Mathematics

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5 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	799-855
Number of pages	57
Journal	Communications in Mathematical Physics
Volume	347
Issue number	3
DOIs	https://doi.org/10.1007/s00220-016-2739-z
State	Published - Nov 1 2016

Bibliographical note

Funding Information:
P. Pylyavskyy was partially supported by NSF Grants DMS-1148634, DMS-1351590, and Sloan Fellowship.

Funding Information:
T. Lam was partially supported by NSF Grants DMS-1160726, DMS-1464693, and a Simons Fellowship.

Funding Information:
R. Inoue was partially supported by JSPS KAKENHI Grant Number 26400037.

Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.

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

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