Anne Schilling, Travis Scrimshaw
Published 2014-09-09Version 1
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 $D_n^{(1)}$.
Perfectness of Kirillov-Reshetikhin Crystals $B^{r,s}$ for types $E_{6}^{(1)}$ and $E_{7}^{(1)}$ with a minuscule node $r$
Rigged configurations as tropicalizations of loop Schur functions
Characterization of ${\cal B}(\infty)$ using marginally large tableaux and rigged configurations in the $A_n$ case via integer sequences
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