Crystal structure on rigged configurations and the filling map

Abstract

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 $D_n^{(1)}$.

45 pages

References in corpus (5)

• T-systems and Y-systems in integrable systems
• Existence of Kirillov-Reshetikhin crystals for nonexceptional types
• A uniform model for Kirillov-Reshetikhin crystals I: Lifting the parabolic quantum Bruhat graph
• Affine crystal structure on rigged configurations of type D_n^(1)
• KKR type bijection for the exceptional affine algebra E_6^{(1)}

Cited by in corpus (8)

• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• A crystal to rigged configuration bijection and the filling map for type $D_4^{(3)}$
• Type $D_n^{(1)}$ rigged configuration bijection
• On higher level Kirillov--Reshetikhin crystals, Demazure crystals, and related uniform models
• Rigged configurations and the $\ast$-involution
• Connecting marginally large tableaux and rigged configurations via crystals
• Identities from representation theory
• Uniform description of the rigged configuration bijection