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.
Bibliographical noteFunding Information:
DOI: 10.1007/S00031-018-9488-3 ∗Partially supported by NSF grant DMS-1303482. ∗∗Partially supported by NSF grants DMS-1148634, DMS-1351590, and Sloan Fellowship. Received January 27, 2017. Accepted June 22, 2018. Published online August 11, 2018. Corresponding Author: Max Glick, e-mail: email@example.com