Ultradiscrete Soliton Systems and Combinatorial Representation Theory

Abstract

This lecture note is intended to be a brief introduction to a recent development on the interplay between the ultradiscrete (or tropical) soliton systems and the combinatorial representation theory. We will concentrate on the simplest cases which admit elementary explanations without losing essential ideas of the theory. In particular we give definitions for the main constructions corresponding to the vector representation of type $A_1^{(1)}$.

18 pages, for proceedings of the conference "Algebraic combinatorics related to Young diagrams and statistical physics" (Kyoto, August 2012)

References in corpus (4)

• Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
• Tau functions in combinatorial Bethe ansatz
• Kirillov--Schilling--Shimozono bijection as energy functions of crystals
• On the X=M=K Conjecture

Cited by in corpus (4)

• Singular Solutions to the Bethe Ansatz Equations and Rigged Configurations
• Soliton decomposition of the Box-Ball System
• Rigged Configurations and Kashiwara Operators
• Bethe's Quantum Numbers And Rigged Configurations