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 . We study the soliton solutions for φn; k/ and explore a duality with the sln-box-ball system.
|Original language||English (US)|
|Number of pages||54|
|Journal||Annales de l'Institut Henri Poincare (D) Combinatorics, Physics and their Interactions|
|State||Published - 2020|
Bibliographical noteFunding Information:
1 Rei Inoue was partially supported by JSPS KAKENHI Grant Number 26400037 and 16H03927. 2 Pavlo Pylyavskyy was partially supported by NSF grants DMS-1148634, DMS-1351590, and Sloan Fellowship.
- Affine symmetric group
- Box-ball system
- Tropical solitons