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Annales de l’Institut Henri Poincaré D


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Volume 7, Issue 2, 2020, pp. 249–302
DOI: 10.4171/AIHPD/86

Published online: 2020-06-05

Soliton cellular automata associated with infinite reduced words

Max Glick[1], Rei Inoue[2] and Pavlo Pylyavskyy[3]

(1) Ohio State University, Columbus, USA
(2) Chiba University, Japan
(3) University of Minnesota, Minneapolis, USA

We consider a family of cellular automata $\Phi(n,k)$ associated with infinite reduced elements on the affine symmetric group $\hat S_n$, which is a tropicalization of the rational maps introduced in [3]. We study the soliton solutions for $\Phi(n,k)$ and explore a duality with the $\mathfrak{sl}_n$-box-ball system.

Keywords: Tropical solitons, affine symmetric group, box-ball system

Glick Max, Inoue Rei, Pylyavskyy Pavlo: Soliton cellular automata associated with infinite reduced words. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 7 (2020), 249-302. doi: 10.4171/AIHPD/86