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

We give a realization of the Kirillov–Reshetikhin crystal $B^{1,s}$ using Nakajima monomials for ${\widehat{\mathfrak{s}\mathfrak{l}}}_n$ using the crystal structure given by Kashiwara. We describe the tensor product $\bigotimes_{i=1}^N B^{1,s_i}$ in terms of a shift of indices, allowing us to recover the Kyoto path model. Additionally, we give a model for the KR crystals $B^{r,1}$ using Nakajima monomials.