# Affine crystal structure on rigged configurations of type $D_{n}^{(1)}$

title={Affine crystal structure on rigged configurations of type \$D\_\{n\}^\{(1)\}\$},
author={Masato Okado and Reiho Sakamoto and Anne Schilling},
journal={Journal of Algebraic Combinatorics},
year={2011},
volume={37},
pages={571-599}
}
• Published 16 September 2011
• Mathematics
• Journal of Algebraic Combinatorics
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 Br,s of type $D_{n}^{(1)}$ for any r,s. We also introduce a representation of Br,s (r≠n−1,n) in terms of tableaux of rectangular shape r×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…
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