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

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. We also give simple non-specialised character formulas with obviously positive coefficients for the three level 2 standard modules.