Séminaire Lotharingien de Combinatoire, 78B.47 (2017), 12 pp.

Emily Gunawan and Travis Scrimshaw

Realization of Kirillov-Reshetikhin Crystals B1,s for sl^n Using Nakajima Monomials

Abstract. We give a realization of the Kirillov-Reshetikhin crystal B1,s for sl^n using Nakajima monomials using the crystal structure given by Kashiwara. We describe the tensor product \bigotimesi=1N B1,si in terms of a shift of indices, allowing us to recover the Kyoto path model. We give a description of the limit of the coherent family of crystals {B1,s}s=1\infty using Nakajima monomials, which allows us to recover the path model for B(\infty). Additionally, we realize the KR crystals Br,1 for sl^n using Nakajima monomials.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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