Realization of affine type A Kirillov-Reshetikhin crystals via polytopes
Representation Theory
2013-09-26 v1 Combinatorics
Quantum Algebra
Abstract
On the polytope defined in Feigin, Fourier, and Littelmann (2011), associated to any rectangle highest weight, we define a structure of an type -crystal. We show, by using the Stembridge axioms, that this crystal is isomorphic to the one obtained from Kashiwara's crystal bases theory. Further we define on this polytope a bijective map and show that this map satisfies the properties of a weak promotion operator. This implies in particular that we provide an explicit realization of Kirillov-Reshetikhin crystals for the affine type via polytopes.
Keywords
Cite
@article{arxiv.1209.6019,
title = {Realization of affine type A Kirillov-Reshetikhin crystals via polytopes},
author = {Deniz Kus},
journal= {arXiv preprint arXiv:1209.6019},
year = {2013}
}