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Mathematics > Algebraic Geometry

arXiv:1504.03448 (math)
[Submitted on 14 Apr 2015 (v1), last revised 21 Jun 2016 (this version, v3)]

Title:Toric networks, geometric $R$-matrices and generalized discrete Toda lattices

Authors:Rei Inoue, Thomas Lam, Pavlo Pylyavskyy
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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.
Comments: 54 pages
Subjects: Algebraic Geometry (math.AG); Combinatorics (math.CO); Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:1504.03448 [math.AG]
  (or arXiv:1504.03448v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1504.03448
Related DOI: https://doi.org/10.1007/s00220-016-2739-z

Submission history

From: Rei Inoue [view email]
[v1] Tue, 14 Apr 2015 08:12:21 UTC (80 KB)
[v2] Mon, 31 Aug 2015 11:55:02 UTC (79 KB)
[v3] Tue, 21 Jun 2016 09:12:59 UTC (78 KB)
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