A crystal theoretic method for finding rigged configurations from paths
Reiho Sakamoto
TL;DR
This paper presents a crystal theoretic reformulation of the KKR bijection, enabling a new approach to analyze rigged configurations and periodic box-ball systems using combinatorial R and energy functions.
Contribution
It introduces a novel crystal theoretic method for deriving rigged configurations from paths, enhancing the analytical tools for integrable systems.
Findings
Reformulation of the KKR map using crystal theory
Application to periodic box-ball systems
Enhanced analytical framework for rigged configurations
Abstract
The Kerov--Kirillov--Reshetikhin (KKR) bijection gives one to one correspondences between the set of highest paths and the set of rigged configurations. In this paper, we give a crystal theoretic reformulation of the KKR map from the paths to rigged configurations, using the combinatorial R and energy functions. This formalism provides tool for analysis of the periodic box-ball systems.
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