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arXiv · 1209.6019

Realization of affine type A Kirillov-Reshetikhin crystals via polytopes

Deniz Kus
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Abstract

On the polytope defined in Feigin, Fourier, and Littelmann (2011), associated to any rectangle highest weight, we define a structure of an type $A_n$-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 $A^{(1)}_n$ via polytopes.

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BibTeXRIS

Deniz Kus. 2012-09-26. Realization of affine type A Kirillov-Reshetikhin crystals via polytopes. https://doi.org/10.1016/j.jcta.2013.08.009

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