Partition identities from higher level crystals of $A_1^{(1)}$

TL;DR

This paper explores perfect crystals for affine Lie algebra $A_1^{(1)}$ using multi-grounded partitions, establishing new partition identities related to Andrews-Gordon and Meurman-Primc identities with simple difference conditions.

Contribution

It introduces novel partition identities derived from higher level crystals of $A_1^{(1)}$, expanding the understanding of crystal structures and partition theory.

Findings

Proved a family of new partition identities with simple difference conditions.

Connected these identities to known Andrews-Gordon and Meurman-Primc identities.

Enhanced the combinatorial understanding of crystals in affine Lie algebras.

Abstract

We study perfect crystals for the standard modules of the affine Lie algebra $A_1^{(1)}$ at all levels using the theory of multi-grounded partitions. We prove a family of partition identities which are reminiscent of the Andrews-Gordon identities and companions to the Meurman-Primc identities, but with simple difference conditions involving absolute values.