Affine structures and a tableau model for E_6 crystals
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Affine structures and a tableau model for E_6 crystals

  • Author(s): Jones, Brant
  • Schilling, Anne
  • et al.

Published Web Location

https://arxiv.org/pdf/0909.2442.pdf
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Abstract

We provide the unique affine crystal structure for type E_6^{(1)} Kirillov-Reshetikhin crystals corresponding to the multiples of fundamental weights s Lambda_1, s Lambda_2, and s Lambda_6 for all s \geq 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_6^{(1)} Dynkin diagram. In addition, we provide a conjecture for the affine crystal structure of type E_7^{(1)} Kirillov-Reshetikhin crystals corresponding to the adjoint node.

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