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={M. Okado and Reiho Sakamoto and A. 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… Expand
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References
SHOWING 1-10 OF 39 REFERENCES
Promotion Operator on Rigged Configurations of Type A
- Mathematics, Computer Science
- Electron. J. Comb.
- 2010
- 13
- PDF
Combinatorial R-matrices for Kirillov--Reshetikhin crystals of type D^{(1)}_n, B^{(1)}_n, A^{(2)}_{2n-1}
- Mathematics
- 2009
- 5
- PDF
Crystal interpretation of Kerov–Kirillov–Reshetikhin bijection II. Proof for
$\mathfrak{sl}_{n}$
case
- Mathematics, Physics
- 2008
- 23
- PDF