### Abstract

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 language | English |
---|---|

Pages (from-to) | 274-308 |

Number of pages | 35 |

Journal | Journal of Mathematical Physics |

Volume | 42 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2001 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'The A<sup>(1)</sup><sub>M</sub> automata related to crystals of symmetric tensors'. Together they form a unique fingerprint.

## Cite this

^{(1)}

_{M}automata related to crystals of symmetric tensors.

*Journal of Mathematical Physics*,

*42*(1), 274-308. https://doi.org/10.1063/1.1322077