Realization of affine type A Kirillov-Reshetikhin crystals via polytopes

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:120

Article

Kus, Deniz

关键词: Quantum affine algebra;    Kirillov-Reshetikhin crystal;    PBW basis;   

DOI  :  10.1016/j.jcta.2013.08.009

来源: Elsevier

【 摘 要 】

On the polytope defined by Feigin, Fourier and Littelmann, associated to any highest weight corresponding to a rectangular partition, we define a crystal structure of type A(n). We show 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 A(n)((1)) via polytopes. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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