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

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