Crystal structure on rigged configurations and the filling map

TL;DR

This paper extends the crystal structure on rigged configurations to all non-exceptional affine types, introduces a new tableaux model for Kirillov-Reshetikhin crystals, and generalizes the filling map concept.

Contribution

It develops a unified crystal structure framework for all non-exceptional affine types and introduces a new tableaux model via the filling map.

Findings

Extended crystal structure to all non-exceptional affine types.

Established a new tableaux model for Kirillov-Reshetikhin crystals.

Generalized the filling map to broader types.

Abstract

In this paper, we extend work of the first author on a crystal structure on rigged configurations of simply-laced type to all non-exceptional affine types using the technology of virtual rigged configurations and crystals. Under the bijection between rigged configurations and tensor products of Kirillov-Reshetikhin crystals specialized to a single tensor factor, we obtain a new tableaux model for Kirillov-Reshetikhin crystals. This is related to the model in terms of Kashiwara-Nakashima tableaux via a filling map, generalizing the recently discovered filling map in type $D_n^{(1)}$.