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DISCRETE SOLITONS IN INFINITE REDUCED WORDS

  • MAX GLICK
  • PAVLO PYLYAVSKYY
Article

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.

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Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA
  2. 2.Department of MathematicsUniversity of MinnesotaMinneapolisUSA

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