Affine crystal structure on rigged configurations of type D_n^(1)
Quantum Algebra
2013-04-02 v3 Combinatorics
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.
Keywords
Cite
@article{arxiv.1109.3523,
title = {Affine crystal structure on rigged configurations of type D_n^(1)},
author = {Masato Okado and Reiho Sakamoto and Anne Schilling},
journal= {arXiv preprint arXiv:1109.3523},
year = {2013}
}
Comments
26 pages, 3 figures. (v3) corrections in the proof reading. (v2) 26 pages; examples added; introduction revised; final version. (v1) 24 pages