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