Affine structures and a tableau model for E6 crystals

We provide the unique affine crystal structure for type 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 Dynkin diagram. In addition, we provide a conjecture for the affine crystal structure of type Kirillov–Reshetikhin crystals corresponding to the adjoint node.