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arxiv: 1610.09224 · v3 · pith:QIICIGTTnew · submitted 2016-10-28 · 🧮 math.CO · math.RT

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

Emily Gunawan , Travis Scrimshaw This is my paper
classification 🧮 math.CO math.RT
keywords monomialsnakajimacrystalcrystalsgivemathfrakmodelwidehat
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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 $\bigotimes_{i=1}^N B^{1,s_i}$ 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.

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