Box-ball system with reflecting end

Abstract

A soliton cellular automaton on a one dimensional semi-infinite lattice with a reflecting end is presented. It extends a box-ball system on an infinite lattice associated with the crystal base of U_q(sl_n). A commuting family of time evolutions are obtained by adapting the K matrices and the double row construction of transfer matrices in solvable lattice models to a crystal setting. Factorized scattering among the left and the right moving solitons and the boundary reflection rule are determined.

32 pages, 12 figure

Cited by in corpus (15)

• Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
• Tau functions in combinatorial Bethe ansatz
• Set theoretic Yang-Baxter & reflection equations and quantum group symmetries
• Tetrahedron and 3D reflection equations from quantized algebra of functions
• Set-theoretical reflection equation: Classification of reflection maps
• Randomized box-ball systems, limit shape of rigged configurations and Thermodynamic Bethe ansatz
• Matrix product solution to the reflection equation associated with a coideal subalgebra of $U_q(A_{n-1}^{(1)})$
• Combinatorial solutions to the reflection equation
• Bethe ansatz at q=0 and periodic box-ball systems
• Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type $A_{n-1}^{(1)}$
• Boundary from bulk integrability in three dimensions: 3D reflection maps from tetrahedron maps
• Generalized hydrodynamics in complete box-ball system for $U_q({\widehat{sl}}_n)$
• Tetrahedron Equation and Quantum $R$ Matrices for $q$-Oscillator Representations Mixing Particles and Holes
• Algebraic structures in set-theoretic Yang-Baxter & reflection equations
• Solution to the reflection equation related to the $\iota$quantum group of type AII