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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:1401.3395 (nlin)
[Submitted on 15 Jan 2014 (v1), last revised 19 Mar 2015 (this version, v2)]

Title:Combinatorial aspects of the conserved quantities of the tropical periodic Toda lattice

Authors:Taichiro Takagi
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Abstract:The tropical periodic Toda lattice (trop p-Toda) is a dynamical system attracting attentions in the area of the interplay of integrable systems and tropical geometry. We show that the Young diagrams associated with trop p-Toda given by two very different definitions are identical. The first definition is given by a Lax representation of the discrete periodic Toda lattice, and the second one is associated with a generalization of the Kerov-Kirillov-Reshetikhin bijection in the combinatorics of the Bethe ansatz. By means of this identification, it is shown for the first time that the Young diagrams given by the latter definition are preserved under time evolution. This result is regarded as an important first step in clarifying the iso-level set structure of this dynamical system in general cases, i.e. not restricted to generic cases.
Comments: 27 pages, 9 figures
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)
Cite as: arXiv:1401.3395 [nlin.SI]
  (or arXiv:1401.3395v2 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.1401.3395
Journal reference: J. Phys. A: Math. Theor. 47 (2014) 395201 (25 pp)
Related DOI: https://doi.org/10.1088/1751-8113/47/39/395201

Submission history

From: Taichiro Takagi [view email]
[v1] Wed, 15 Jan 2014 00:58:38 UTC (194 KB)
[v2] Thu, 19 Mar 2015 23:35:22 UTC (197 KB)
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