Soliton cellular automata associated with infinite reduced words

2017/12/25 by Glick, Max, Inoue, Rei, Pylyavskyy, Pavlo
#Combinatorics (math.CO) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1712.08989

Abstract

We consider a family of cellular automata Φ(n,k) associated with infinite reduced elements on the affine symmetric group S_n, which is a tropicalization of the rational maps introduced by two of the authors. We study the soliton solutions for Φ(n,k) and explore a `duality' with the \mathfraksl_n-box-ball system.

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