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

@article{Okado2011AffineCS,
  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}
}
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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20 Citations

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