RSK correspondence and classically irreducible Kirillov-Reshetikhin crystals

TL;DR

This paper introduces a new combinatorial model for Kirillov-Reshetikhin crystals of type A_n^{(1)} using the RSK algorithm, simplifying the description of their affine crystal structure.

Contribution

It provides a novel combinatorial framework for these crystals that avoids the use of promotion operators, extending to exceptional nodes in classical types.

Findings

New combinatorial model based on non-negative integral matrices

Simplified description of affine crystal structure

Extension to exceptional nodes in classical types

Abstract

We give a new combinatorial model of the Kirillov-Reshetikhin crystals of type $A_n^{(1)}$ in terms of non-negative integral matrices based on the classical RSK algorithm, which has a simple description of the affine crystal structure without using a promotion operator. We also have a similar description of the Kirillov-Reshetikhin crystals associated to exceptional nodes in the Dynkin diagrams of classical affine or non-exceptional type.