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Crystal structure on rigged configurations and the filling map

  • Author(s): Schilling, A
  • Scrimshawy, T
  • et al.

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© 2015, Australian National University. All rights reserved. In this paper, we extend work of the first author on a crystal structure on rigged con_gurations of simply-laced type to all non-exceptional affine types using the technology of virtual rigged con_gurations 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 typeD(1)n

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