DISCRETE SOLITONS IN INFINITE REDUCED WORDS

Max Glick, Pavlo Pylyavskyy

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We consider a discrete dynamical system where the roles of the states and the carrier are played by translations in an affine Weyl group of type A. The Coxeter generators are enriched by parameters, and the interactions with the carrier are realized using Lusztig’s braid move (a, b, c) ↦ (bc/(a+c), a+c, ab/(a+c)). We use wiring diagrams on a cylinder to interpret chamber variables as τ-functions. This allows us to realize our systems as reductions of the Hirota bilinear difference equation and thus obtain N-soliton solutions.

Original languageEnglish (US)
Pages (from-to)31-66
Number of pages36
JournalTransformation Groups
Volume24
Issue number1
DOIs
StatePublished - Mar 15 2019

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