# 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…

## 20 Citations

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We establish a bijection between the set of rigged configurations and the set of tensor products of Kirillov–Reshetikhin crystals of type $$D^{(1)}_n$$Dn(1) in full generality. We prove the…

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We construct an explicit algorithm of the static-preserving bijection between the rigged configurations and the highest weight paths of the form (B2,1)⊗L in the G (1) 2 adjoint crystals.

Uniform description of the rigged configuration bijection

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We give a uniform description of the bijection $$\Phi $$ Φ from rigged configurations to tensor products of Kirillov–Reshetikhin crystals of the form $$\bigotimes _{i=1}^N B^{r_i,1}$$ ⨂ i = 1 N B r i…

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Rigged Configurations and Kashiwara Operators

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For types A (1) and D (1) n we prove that the rigged configuration bijection in- tertwines the classical Kashiwara operators on tensor products of the arbitrary Kirillov{ Reshetikhin crystals and the…

Connecting Marginally Large Tableaux and Rigged Configurations via Crystals

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- 2015

We show that the bijection from rigged configurations to tensor products of Kirillov-Reshetikhin crystals extends to a crystal isomorphism between the B(∞)$B(\infty )$ models given by rigged…

Tableau models for semi-infinite Bruhat order and level-zero representations of quantum affine algebras.

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We prove that semi-infinite Bruhat order on an affine Weyl group is completely determined from those on the quotients by affine Weyl subgroups associated with various maximal (standard) parabolic…

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