# Crystals from 5-vertex ice models

## TL;DR

This paper constructs a crystal structure on 5-vertex ice models with specific boundary conditions and proves its isomorphism to the crystal of an irreducible representation of highest weight , , , , .

## Contribution

It introduces a novel crystal structure on 5-vertex ice models and establishes its equivalence to known algebraic crystals for , , , ,  representations.

## Key findings

- Crystal structure on 5-vertex ice models is well-defined.
- The crystal is isomorphic to the irreducible representation of highest weight , , , , .
- Provides a combinatorial model for these algebraic structures.

## Abstract

Given a partition $\lambda$ corresponding to a dominant integral weight of $\mathfrak{sl}_n$, we define the structure of crystal on the set of 5-vertex ice models satisfying certain boundary conditions associated to $\lambda$. We then show that the resulting crystal is isomorphic to that of the irreducible representation of highest weight $\lambda$.