The AM(1) automata related to crystals of symmetric tensors

DOI10.1063/1.1322077zbMath1032.17021arXivmath/9912209OpenAlexW1635811266MaRDI QIDQ2774658

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Publication date: 26 February 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9912209

zbMATH Keywords

soliton solutionsscattering matricesquantum affine algebrasoliton cellular automatoncombinatorial \(R\) matricescrystals of symmetric tensor representationsdiscrete Kadomtsev-Petviashivili equationgeneralized box-ball systempiecewise linear evolution equation

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Cellular automata (computational aspects) (68Q80)

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Cites Work

• Kostka polynomials and energy functions in solvable lattice models
• Perfect crystals of quantum affine Lie algebras
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Toda-type cellular automaton and its \(N\)-soliton solution
• Crystalizing the q-analogue of universal enveloping algebras
• AFFINE CRYSTALS AND VERTEX MODELS
• Box and ball system with a carrier and ultradiscrete modified KdV equation
• Darboux and binary Darboux transformations for the nonautonomous discrete KP equation
• Crystallization of the Bogoyavlensky Lattice
• Conserved Quantities of a Class of Nonlinear Difference-Difference Equations
• Box and ball system as a realization of ultradiscrete nonautonomous KP equation
• Supersymmetric extension of the integrable box-ball system
• Proof of solitonical nature of box and ball systems by means of inverse ultra-discretization
• Soliton cellular automata associated with crystal bases

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