Combinatorial Bethe ansatz and generalized periodic box-ball system
arXiv:0708.3287 · doi:10.1142/S0129055X08003365
Abstract
We reformulate the Kerov-Kirillov-Reshetikhin (KKR) map in the combinatorial Bethe ansatz from paths to rigged configurations by introducing local energy distribution in crystal base theory. Combined with an earlier result on the inverse map, it completes the crystal interpretation of the KKR bijection for U_q(\hat{sl}_2). As an application, we solve an integrable cellular automaton, a higher spin generalization of the periodic box-ball system, by an inverse scattering method and obtain the solution of the initial value problem in terms of the ultradiscrete Riemann theta function.
27 pages
References in corpus (11)
- The A^{(1)}_M automata related to crystals of symmetric tensors
- Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
- Soliton Cellular Automata Associated With Crystal Bases
- Energy Functions in Box Ball Systems
- Fundamental Cycle of a Periodic Box-Ball System
- On a Periodic Soliton Cellular Automaton
- New fermionic formula for unrestricted Kostka polynomials
- Tau functions in combinatorial Bethe ansatz
- Bethe ansatz and inverse scattering transform in a periodic box-ball system
- On the initial value problem of a periodic box-ball system
- Combinatorial Bethe ansatz and ultradiscrete Riemann theta function with rational characteristics