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.

中文翻译：

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Kirillov–Reshetikhin晶体B 1，s为 ̂ n $ \ widehat {\ mathfrak {s} \ mathfrak {l}} _ {n} $使用Nakajima Monomials

我们给出一个实现基里洛夫-Reshetikhin晶体的乙^1，š使用中岛单项式为\（\ widehat {\ mathfrak {S} \ mathfrak {1}} _ {N} \）使用由柏原给定的晶体结构。我们根据索引的偏移量来描述张量积\（\ bigotimes _ {i = 1} ^ {N} B ^ {1，s_ {i}} \），从而使我们能够恢复Kyoto路径模型。此外，我们使用中岛单项式给出了KR晶体B ^r，1的模型。