Toward Berenstein-Zelevinsky data in affine type $A$, part III: Proof of the connectedness

TL;DR

This paper proves the connectedness of a specific crystal structure in affine type A, advancing the understanding of Berenstein-Zelevinsky data in this mathematical context.

Contribution

It provides a proof of the connectedness property for the crystal introduced in earlier works, contributing to the theory of affine type A crystals.

Findings

Proved the connectedness of the crystal in affine type A.

Confirmed the structure's coherence and connectivity.

Extended the mathematical framework of Berenstein-Zelevinsky data.

Abstract

We prove the connectedness of the crystal, which we introduced in our previous works.