Tau functions in combinatorial Bethe ansatz

Abstract

We introduce ultradiscrete tau functions associated with rigged configurations for A^{(1)}_n. They satisfy an ultradiscrete version of the Hirota bilinear equation and play a role analogous to a corner transfer matrix for the box-ball system. As an application, we establish a piecewise linear formula for the Kerov-Kirillov-Reshetikhin bijection in the combinatorial Bethe ansatz. They also lead to general N-soliton solutions of the box-ball system.

52 pages

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Cited by in corpus (25)

• Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
• Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
• Singular Solutions to the Bethe Ansatz Equations and Rigged Configurations
• Affine crystal structure on rigged configurations of type D_n^(1)
• Kirillov--Schilling--Shimozono bijection as energy functions of crystals
• Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case
• Ultradiscretization of a solvable two-dimensional chaotic map associated with the Hesse cubic curve
• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• Bethe Ansatz, Inverse Scattering Transform and Tropical Riemann Theta Function in a Periodic Soliton Cellular Automaton for A^{(1)}_n
• Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations
• KKR type bijection for the exceptional affine algebra E_6^{(1)}
• Ultradiscretization of solvable one-dimensional chaotic maps
• Stable Rigged Configurations for Quantum Affine Algebras of Nonexceptional Types
• Box-Basket-Ball Systems
• A uniform approach to soliton cellular automata using rigged configurations
• Combinatorial Bethe ansatz and generalized periodic box-ball system
• Ultradiscrete Soliton Systems and Combinatorial Representation Theory
• Rigged configurations as tropicalizations of loop Schur functions
• Finding Rigged Configurations From Paths
• Uniform description of the rigged configuration bijection
• Kirillov-Reshetikhin modules of generalized quantum group of type $A$
• Tropical Krichever construction for the non-periodic box and ball system
• Paths and Kostka--Macdonald Polynomials
• A crystal theoretic method for finding rigged configurations from paths
• Similarity and Kirillov-Schilling-Shimozono bijection