Brant Jones ; Anne Schilling
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Affine structures and a tableau model for E6 crystals
dmtcs:2809 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2010,
DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
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https://doi.org/10.46298/dmtcs.2809
Affine structures and a tableau model for E6 crystalsConference paper
Authors: Brant Jones 1; Anne Schilling 1
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Brant Jones;Anne Schilling
1 Department of Mathematics [Univ California Davis]
We provide the unique affine crystal structure for type E(1)6 Kirillov―Reshetikhin crystals corresponding to the multiples of fundamental weights sΛ1,sΛ2, and sΛ6 for all s≥1 (in Bourbaki's labeling of the Dynkin nodes, where 2 is the adjoint node). Our methods introduce a generalized tableaux model for classical highest weight crystals of type E and use the order three automorphism of the affine E(1)6 Dynkin diagram. In addition, we provide a conjecture for the affine crystal structure of type E(1)7 Kirillov―Reshetikhin crystals corresponding to the adjoint node.