Toward Berenstein-Zelevinsky data in affine type $A$, part II: Explicit description

TL;DR

This paper provides an explicit description of affine Berenstein-Zelevinsky data using Lusztig data for affine type A, extending previous constructions to a more detailed combinatorial framework.

Contribution

It introduces an explicit combinatorial description of affine Berenstein-Zelevinsky data via Lusztig data, advancing the understanding of affine type A structures.

Findings

Explicit description of affine Berenstein-Zelevinsky data

Representation of data through Lusztig data of affine type A

Extension of previous affine data constructions

Abstract

In the present paper, we give an explicit description of the affine analogs of Berenstein-Zelevinsky data constructed in our previous paper: Toward Berenstein-Zelevinsky data in affine type $A$, I: Construction of affine analogs (arXiv:1009.4526), in terms of certain collections of nonnegative integers, which we call Lusztig data of type $A_{l-1}^{(1)}$.