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

G. Hatayama, K. Hikami, R. Inoue, A. Kuniba, T. Takagi, T. Tokihiro

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80 Citations (Scopus)


A soliton cellular automaton associated with crystals of symmetric tensor representations of the quantum affine algebra U′q(A(1)M) is introduced. It is a crystal theoretic formulation of the generalized box-ball system in which capacities of boxes and carriers are arbitrary and inhomogeneous. Scattering matrices of two solitons coincide with the combinatorial R matrices of U′q(A(1)M-1). A piecewise linear evolution equation of the automaton is identified with an ultradiscrete limit of the nonautonomous discrete Kadomtsev-Petviashivili equation. A class of N soliton solutions is obtained through the ultradiscretization of soliton solutions of the latter.

Original languageEnglish
Pages (from-to)274-308
Number of pages35
JournalJournal of Mathematical Physics
Issue number1
Publication statusPublished - Jan 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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