Partition models for the crystal of the basic $U_q(\hat{\mathfrak{sl}}_n)$-module

TL;DR

This paper constructs a broad family of partition-based models for the crystal of the basic quantum affine algebra module, unifying several known models including the ladder crystal.

Contribution

It introduces an uncountable family of partition models for the crystal, encompassing existing models like the $n$-regular, $n$-restricted, and Berg's ladder crystal.

Findings

Includes the usual $n$-regular and $n$-restricted models

Incorporates Berg's ladder crystal as a special case

Establishes a unifying framework for crystal models

Abstract

For each $n\geqslant3$, we construct an uncountable family of models of the crystal of the basic $U_q(\hat{\mathfrak{sl}}_n)$-module. These models are all based on partitions, and include the usual $n$-regular and $n$-restricted models, as well as Berg's ladder crystal, as special cases.