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

Abstract

We give a realization of the Kirillov--Reshetikhin crystal $B^{1,s}$ using Nakajima monomials for ${\widehat{\mathfrak{sl}}}_n$ using the crystal structure given by Kashiwara. We describe the tensor product ${⨂}_{i=1}^N{B}^{1,s_i}$ 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.

24 pages, 6 figures; v2 improved introduction, added more figures, and other misc improvements; v3 changes from referee reports

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