Promotion operator on rigged configurations of type A

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Schilling, Anne
Wang, Qiang
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Abstract
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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.
Comment: 37 pages
Keywords
Mathematics - Combinatorics, Mathematics - Quantum Algebra, 05E15
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