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arXiv · 1709.10195

Linearization of the box-ball system: an elementary approach

Saburo Kakei·Jonathan J. C. Nimmo·Satoshi Tsujimoto·Ralph Willox
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Abstract

Kuniba, Okado, Takagi and Yamada have found that the time-evolution of the Takahashi-Satsuma box-ball system can be linearized by considering rigged configurations associated with states of the box-ball system. We introduce a simple way to understand the rigged configuration of $\mathfrak{sl}_2$-type, and give an elementary proof of the linearization property. Our approach can be applied to a box-ball system with finite carrier, which is related to a discrete modified KdV equation, and also to the combinatorial $R$-matrix of $A_1^{(1)}$-type. We also discuss combinatorial statistics and related fermionic formulas associated with the states of the box-ball systems. A fermionic-type formula we obtain for the finite carrier case seems to be new.

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Saburo Kakei, Jonathan J. C. Nimmo, Satoshi Tsujimoto, Ralph Willox. 2017-12-30. Linearization of the box-ball system: an elementary approach. https://arxiv.org/abs/1709.10195

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