Analysis of a particle antiparticle description of a soliton cellular automaton

DOI10.1063/1.2161390zbMath1111.82035arXivmath-ph/0312069OpenAlexW2058901945MaRDI QIDQ3441604

Taichiro Takagi

Publication date: 16 May 2007

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

Full work available at URL: https://arxiv.org/abs/math-ph/0312069

Mathematics Subject Classification ID

Applications of Lie (super)algebras to physics, etc. (17B81) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Dynamical aspects of cellular automata (37B15)

Cites Work

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• Crystals for Demazure modules of classical affine Lie algebras
• Crystal bases of modified quantized enveloping algebra
• Combinatorial \(R\) matrices for a family of crystals: \(B_n^{(1)}\), \(D_n^{(1)}\), \(A_{2n}^{(2)}\) and \(D_{n+1}^{(2)}\) cases
• Tropical \(R\) and tau functions
• Box-ball systems and Robinson-Schensted-Knuth correspondence
• Crystalizing the q-analogue of universal enveloping algebras
• Simple algorithm for factorized dynamics of the $\frak{g}_n$-automaton
• The AM(1) automata related to crystals of symmetric tensors
• Box and ball system with a carrier and ultradiscrete modified KdV equation
• Factorization, reduction and embedding in integrable cellular automata
• Box and ball system as a realization of ultradiscrete nonautonomous KP equation
• Soliton cellular automata associated with crystal bases
• Factorization of combinatorial \(R\) matrices and associated cellular automata.

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