A generalization of the alcove model and its applications
Abstract
The alcove model of the first author and A. Postnikov uniformly describes highest weight crystals of semisimple Lie algebras. We construct a generalization, called the quantum alcove model. In joint work of the first author with S. Naito, D. Sagaki, A. Schilling, and M. Shimozono, this was shown to uniformly describe tensor products of column shape Kirillov-Reshetikhin crystals in all untwisted affine types; moreover, an efficient formula for the corresponding energy function is available. In the second part of this paper, we specialize the quantum alcove model to types and . We give explicit affine crystal isomorphisms from the specialized quantum alcove model to the corresponding tensor products of column shape Kirillov-Reshetikhin crystals, which are realized in terms of Kashiwara-Nakashima columns.
Keywords
Cite
@article{arxiv.1112.2216,
title = {A generalization of the alcove model and its applications},
author = {Cristian Lenart and Arthur Lubovsky},
journal= {arXiv preprint arXiv:1112.2216},
year = {2013}
}
Comments
Ver2: Replaced extended abstract with full paper Ver3: Introduction and abstract expanded and made sharper. Signature rule in types A and C had small inaccuracies. Proposition 2.9, more on perfect crystals. Expanded the main Theorem 3.8 (and its proof). Expanded the "Main applications" section. Some changes in the proofs of Prop. 4.14-4.16