2017/09/28 by Kakei, Saburo, Nimmo, Jonathan J. C., Tsujimoto, Satoshi +1
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1709.10195
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 \mathfraksl2-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 A1(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.