Partition identities from higher level crystals of A₁⁽¹⁾

This is the authors' abstract. We don't add key points for this paper.

We study perfect crystals for the standard modules of the affine Lie algebra A₁⁽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.