Rigged configurations and the ⁎-involution for generalized Kac–Moody algebras

We construct a uniform model for highest weight crystals and B(∞) for generalized Kac–Moody algebras using rigged configurations. We also show an explicit description of the ⁎-involution on rigged configurations for B(∞): that the ⁎-involution interchanges the rigging and the corigging. We do this by giving a recognition theorem for B(∞) using the ⁎-involution. As a consequence, we also characterize B(λ) as a subcrystal of B(∞) using the ⁎-involution.