Geodesic
Affine crystal structure on rigged configurations of type $D_{n}^{(1)}$
Journal of Algebraic Combinatorics, Tome 37 (2013) no. 3, pp. 571-599.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Extending the work in Schilling (Int. Math. Res. Not. 2006:97376, 2006), we introduce the affine crystal action on rigged configurations which is isomorphic to the Kirillov-Reshetikhin crystal B $^{ r,s }$ of type $D_{n}^{(1)}$ for any r,s. We also introduce a representation of B $^{ r,s } (r\neq n - 1,n)$ in terms of tableaux of rectangular shape r$\times s$, which we coin Kirillov-Reshetikhin tableaux (using a nontrivial analogue of the type A column splitting procedure) to construct a bijection between elements of a tensor product of Kirillov-Reshetikhin crystals and rigged configurations.
Keywords: quantum algebras, crystal bases, rigged configurations 
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     author = {Okado, Masato and Sakamoto, Reiho and Schilling, Anne},
     title = {Affine crystal structure on rigged configurations of type $D_{n}^{(1)}$},
     journal = {Journal of Algebraic Combinatorics},
     pages = {571--599},
     publisher = {mathdoc},
     volume = {37},
     number = {3},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2013__37_3_a0/}
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Okado, Masato; Sakamoto, Reiho; Schilling, Anne. Affine crystal structure on rigged configurations of type $D_{n}^{(1)}$. Journal of Algebraic Combinatorics, Tome 37 (2013) no. 3, pp. 571-599. http://geodesic.mathdoc.fr/item/JAC_2013__37_3_a0/