Connecting marginally large tableaux and rigged configurations via crystals

TL;DR

This paper establishes a crystal isomorphism linking rigged configurations and marginally large tableaux, expanding the understanding of their relationship within the framework of $B()$ models in crystal theory.

Contribution

It extends the bijection from rigged configurations to tensor products of Kirillov-Reshetikhin crystals to a full crystal isomorphism involving $B()$ models.

Findings

Rigged configurations and marginally large tableaux are shown to be crystal isomorphic.

The bijection from rigged configurations to tensor products extends to a broader crystal isomorphism.

The work deepens the understanding of the structure of $B()$ models in crystal theory.

Abstract

We show that the bijection from rigged configurations to tensor products of Kirillov-Reshetikhin crystals extends to a crystal isomorphism between the $B(\infty)$ models given by rigged configurations and marginally large tableaux.