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

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

Research output: Contribution to journalArticle

75 Citations (Scopus)

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 languageEnglish
Pages (from-to)274-308
Number of pages35
JournalJournal of Mathematical Physics
Volume42
Issue number1
DOIs
Publication statusPublished - Jan 1 2001
Externally publishedYes

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

    Hatayama, G., Hikami, K., Inoue, R., Kuniba, A., Takagi, T., & Tokihiro, T. (2001). The A(1)M automata related to crystals of symmetric tensors. Journal of Mathematical Physics, 42(1), 274-308. https://doi.org/10.1063/1.1322077