Realization of affine type A Kirillov-Reshetikhin crystals via polytopes
Abstract
On the polytope defined in Feigin, Fourier, and Littelmann (2011), associated to any rectangle highest weight, we define a structure of an type An-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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