A set of action-angle variables for a soliton cellular automaton is obtained.
It is identified with the rigged configuration, a well-known object in Bethe
ansatz. Regarding it as the set of scattering data an inverse scattering method
to solve initial value problems of this automaton is presented. By considering
partition functions for this system a new interpretation of a fermionic
character formula is obtained.Comment: 29 pages, LaTe