Promotion Operator on Rigged Configurations of Type $A$

Abstract

In an earlier paper of the first author, 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.