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=0 as well as the direct and the inverse scattering (Gel'fand-Levitan) map in the associated soliton cellular automaton. 
Atsuo Kuniba, Masato Okado, Reiho Sakamoto, Taichiro Takagi, Yasuhiko   Yamada