Geodesic
Promotion operator on rigged configurations of type \(A\)
The electronic journal of combinatorics, Tome 17 (2010)

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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.
DOI : 10.37236/296
Classification : 05E10, 17B37, 82B23
Mots-clés : promotion operator, crystal structure 
Anne Schilling; Qiang Wang. Promotion operator on rigged configurations of type \(A\). The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/296
@article{10_37236_296,
     author = {Anne Schilling and Qiang Wang},
     title = {Promotion operator on rigged configurations of type {\(A\)}},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/296},
     zbl = {1193.05162},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/296/}
}
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