A uniform approach to soliton cellular automata using rigged configurations
arXiv:1706.02443 · doi:10.1007/s00023-019-00773-8
Abstract
For soliton cellular automata, we give a uniform description and proofs of the solitons, the scattering rule of two solitons, and the phase shift using rigged configurations in a number of special cases. In particular, we prove these properties for the soliton cellular automata using $B^{r,1}$ when $r$ is adjacent to $0$ in the Dynkin diagram or there is a Dynkin diagram automorphism sending $r$ to $0$.
37 pages, 3 figures, 4 tables