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) |
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Pages (from-to) | 799-855 |
Number of pages | 57 |
Journal | Communications in Mathematical Physics |
Volume | 347 |
Issue number | 3 |
DOIs | |
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.