Finding Rigged Configurations From Paths
Reiho Sakamoto
TL;DR
This paper reviews the connection between tensor products of crystals and rigged configurations, providing an intuitive understanding of the inverse scattering formalism for periodic box-ball systems.
Contribution
It offers a reformulation of the map using the energy function and visualizes the inverse scattering process for integrable systems.
Findings
Reformulation of the crystal to rigged configuration map
Intuitive visualization of inverse scattering for box-ball systems
Connection between energy functions and system dynamics
Abstract
We review reformulation of the map from tensor product of crystals to the rigged configurations in terms of the energy function of affine crystals. Especially, we give intuitive picture of the inverse scattering formalism for the periodic box-ball systems formulated by Kuniba-Takagi-Takenouchi (arXiv:math/0602481v2).
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons