  Recently, the analogue of the promotion operator on crystals of type A under
a generalization of the bijection of Kerov, Kirillov and Reshetikhin between
crystals (or Littlewood--Richardson tableaux) and rigged configurations was
proposed. In this paper, we give a proof of this conjecture. This shows in
particular that the bijection between tensor products of type A_n^{(1)}
crystals and (unrestricted) rigged configurations is an affine crystal
isomorphism.
