Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations

Abstract

There are two distinct approaches to the study of initial value problem of the periodic box-ball systems. One way is the rigged configuration approach due to Kuniba--Takagi--Takenouchi and another way is the 10-elimination approach due to Mada--Idzumi--Tokihiro. In this paper, we describe precisely interrelations between these two approaches.

16 pages, final version, minor revision

References in corpus (13)

• The A^{(1)}_M automata related to crystals of symmetric tensors
• Energy Functions in Box Ball Systems
• Fundamental Cycle of a Periodic Box-Ball System
• On a Periodic Soliton Cellular Automaton
• Tau functions in combinatorial Bethe ansatz
• Bethe ansatz and inverse scattering transform in a periodic box-ball system
• Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case
• The Bethe ansatz in a periodic box-ball system and the ultradiscrete Riemann theta function
• On the initial value problem of a periodic box-ball system
• A tropical analogue of Fay's trisecant identity and the ultra-discrete periodic Toda lattice
• Combinatorial Bethe ansatz and ultradiscrete Riemann theta function with rational characteristics
• Finding Rigged Configurations From Paths
• Paths and Kostka--Macdonald Polynomials

Cited by in corpus (6)

• Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
• Bethe Ansatz, Inverse Scattering Transform and Tropical Riemann Theta Function in a Periodic Soliton Cellular Automaton for A^{(1)}_n
• A uniform approach to soliton cellular automata using rigged configurations
• Fermionic partition functions for a periodic soliton cellular automaton
• Tropical Krichever construction for the non-periodic box and ball system
• Linearization of the box-ball system with box capacity L