Kirillov--Schilling--Shimozono bijection as energy functions of crystals

Abstract

The Kirillov--Schilling--Shimozono (KSS) bijection appearing in theory of the Fermionic formula gives an one to one correspondence between the set of elements of tensor products of the Kirillov--Reshetikhin crystals (called paths) and the set of rigged configurations. It is a generalization of Kerov--Kirillov--Reshetikhin bijection and plays inverse scattering formalism for the box-ball systems. In this paper, we give an algebraic reformulation of the KSS map from the paths to rigged configurations, using the combinatorial R and energy functions of crystals. It gives a characterization of the KSS bijection as an intrinsic property of tensor products of crystals.

arXiv comment31 pages, final version, expositions much detailed

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Cited by in corpus (10)

• Rigged Configurations and Kashiwara Operators
• Randomized box-ball systems, limit shape of rigged configurations and Thermodynamic Bethe ansatz
• Bethe Ansatz, Inverse Scattering Transform and Tropical Riemann Theta Function in a Periodic Soliton Cellular Automaton for A^{(1)}_n
• Box-Basket-Ball Systems
• Ultradiscrete Soliton Systems and Combinatorial Representation Theory
• Finding Rigged Configurations From Paths
• Generalized hydrodynamics in complete box-ball system for $U_q({\widehat{sl}}_n)$
• Bethe's Quantum Numbers And Rigged Configurations
• Promotion operator on rigged configurations of type A
• Paths and Kostka--Macdonald Polynomials