Crystal interpretation of Kerov–Kirillov–Reshetikhin bijection

The Kerov–Kirillov–Reshetikhin (KKR) bijection is the crux in proving fermionic formulas. It is defined by a combinatorial algorithm on rigged configurations and highest paths. We reformulate the KKR bijection as a vertex operator by purely using combinatorial R   in crystal base theory. The result is viewed as a nested Bethe ansatz at q=0q=0 as well as the direct and the inverse scattering (Gel'fand–Levitan) map in the associated soliton cellular automaton.