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

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.