Promotion operator on rigged configurations of type A
Abstract
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 An(1) crystals and (unrestricted) rigged configurations is an affine crystal isomorphism.
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