English

Affine structures and a tableau model for E_6 crystals

Combinatorics 2011-02-07 v2 Quantum Algebra

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.

Keywords

Cite

@article{arxiv.0909.2442,
  title  = {Affine structures and a tableau model for E_6 crystals},
  author = {Brant Jones and Anne Schilling},
  journal= {arXiv preprint arXiv:0909.2442},
  year   = {2011}
}

Comments

28 pages

R2 v1 2026-06-21T13:45:55.009Z