The A(M)((1)) automata related to crystals of symmetric tensors

A soliton cellular automaton associated with crystals of symmetric tensor r epresentations of the quantum affine algebra U-q'(A(M)((1))) is introduced. It is a crystal theoretic formulation of the generalized box-ball system i n which capacities of boxes and carriers are arbitrary and inhomogeneous. S cattering matrices of two solitons coincide with the combinatorial R matric es of U-q'(A(M-1)((1))). A piecewise linear evolution equation of the autom aton is identified with an ultradiscrete limit of the nonautonomous discret e Kadomtsev-Petviashivili equation. A class of N soliton solutions is obtai ned through the ultradiscretization of soliton solutions of the latter. (C) 2001 American Institute of Physics.