In this paper, we extend work of the first author on a crystal structure on rigged configurations of simply-laced type to all non-exceptional affine types using the technology of virtual rigged configurations and crystals. Under the bijection between rigged configurations and tensor products of Kirillov--Reshetikhin crystals specialized to a single tensor factor, we obtain a new tableaux model for Kirillov--Reshetikhin crystals. This is related to the model in terms of Kashiwara--Nakashima tableaux via a filling map, generalizing the recently discovered filling map in type $D_n^{(1)}$.
@article{10_37236_4674,
author = {Anne Schilling and Travis Scrimshaw},
title = {Crystal structure on rigged configurations and the filling map},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/4674},
zbl = {1310.05021},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4674/}
}
TY - JOUR
AU - Anne Schilling
AU - Travis Scrimshaw
TI - Crystal structure on rigged configurations and the filling map
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/4674/
DO - 10.37236/4674
ID - 10_37236_4674
ER -
%0 Journal Article
%A Anne Schilling
%A Travis Scrimshaw
%T Crystal structure on rigged configurations and the filling map
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/4674/
%R 10.37236/4674
%F 10_37236_4674
Anne Schilling; Travis Scrimshaw. Crystal structure on rigged configurations and the filling map. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4674
