Affine crystal structure on rigged configurations of type D_n^(1)

Abstract

Extending the work arXiv:math/0508107, 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 not equal to n-1,n) in terms of tableaux of rectangular shape r x s, which we coin Kirillov-Reshetikhin tableaux (using a non-trivial 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.

26 pages, 3 figures. (v3) corrections in the proof reading. (v2) 26 pages; examples added; introduction revised; final version. (v1) 24 pages

References in corpus (8)

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• Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
• X=M for symmetric powers
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• Combinatorial structure of Kirillov-Reshetikhin crystals of type D_n(1), B_n(1), A_{2n-1}(2)
• KKR type bijection for the exceptional affine algebra E_6^{(1)}
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• Rigged configurations and the $\ast$-involution
• Connecting marginally large tableaux and rigged configurations via crystals
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• Virtualization map for the Littelmann path model
• Uniform description of the rigged configuration bijection
• Rigged Configuration Descriptions of the Crystals B(infinity) and B(lambda) for Special Linear Lie Algebras
• An Explicit Algorithm of Rigged Configuration Bijection for the Adjoint Crystal of Type $G_2^{(1)}$