Soliton cellular automata associated with infinite reduced words

Max Glick; Rei Inoue; Pavlo Pylyavskyy

doi:10.4171/AIHPD/86

Soliton cellular automata associated with infinite reduced words

Max Glick
, Rei Inoue
, Pavlo Pylyavskyy

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a family of cellular automata φn; k/ associated with infinite reduced elements on the affine symmetric group Ŝ_n, which is a tropicalization of the rational maps introduced in [3]. We study the soliton solutions for φn; k/ and explore a duality with the sl_n-box-ball system.

Original language	English (US)
Pages (from-to)	249-302
Number of pages	54
Journal	Annales de l'Institut Henri Poincare (D) Combinatorics, Physics and their Interactions
Volume	7
Issue number	2
DOIs	https://doi.org/10.4171/AIHPD/86
State	Published - 2020

Bibliographical note

Publisher Copyright:
© European Mathematical Society.

Keywords

Affine symmetric group
Box-ball system
Tropical solitons

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10.4171/AIHPD/86

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abstract = "We consider a family of cellular automata φn; k/ associated with infinite reduced elements on the affine symmetric group Ŝn, which is a tropicalization of the rational maps introduced in [3]. We study the soliton solutions for φn; k/ and explore a duality with the sln-box-ball system.",

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AU - Inoue, Rei

AU - Pylyavskyy, Pavlo

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2020

Y1 - 2020

N2 - We consider a family of cellular automata φn; k/ associated with infinite reduced elements on the affine symmetric group Ŝn, which is a tropicalization of the rational maps introduced in [3]. We study the soliton solutions for φn; k/ and explore a duality with the sln-box-ball system.

AB - We consider a family of cellular automata φn; k/ associated with infinite reduced elements on the affine symmetric group Ŝn, which is a tropicalization of the rational maps introduced in [3]. We study the soliton solutions for φn; k/ and explore a duality with the sln-box-ball system.

KW - Affine symmetric group

KW - Box-ball system

KW - Tropical solitons

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Soliton cellular automata associated with infinite reduced words

Abstract

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