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

# Emily Gunawan and Travis Scrimshaw

# Realization of Kirillov-Reshetikhin Crystals *B*^{1,s} for
**sl**^{^}_{n} Using Nakajima Monomials

**Abstract.**
We give a realization of the Kirillov-Reshetikhin crystal
*B*^{1,s}
for
**sl**^{^}_{n} using Nakajima monomials using the
crystal structure given by Kashiwara. We describe the tensor product
*\bigotimes*_{i=1}^{N}
*B*^{1,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
{*B*^{1,s}}_{s=1}^{\infty}
using Nakajima monomials, which allows us
to recover the path model for
*B*(*\infty*). Additionally, we realize
the KR crystals
*B*^{r,1} for
**sl**^{^}_{n}
using Nakajima monomials.

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

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