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We give a realization of the Kirillov--Reshetikhin crystal $B^{1,s}$ usingNakajima monomials for $\widehat{\mathfrak{sl}}_n$ using the crystal structuregiven by Kashiwara. We describe the tensor product $\bigotimes_{i=1}^NB^{1,s_i}$ in terms of a shift of indices, allowing us to recover the Kyotopath model. Additionally, we give a model for the KR crystals $B^{r,1}$ usingNakajima monomials.

Kirillov-Reshetikhin crystals $B^{1,s}$ for $\widehat{\mathfrak{sl}}_n$ using Nakajima monomials