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arXiv · 2608.27949

Special Kirillov-Reshetikhin crystals

Il-Seung Jang·Travis Scrimshaw
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Abstract

We give a uniform realization of Kirillov-Reshetikhin crystals $B^{r,s}$, in terms of PBW crystals, for all affine types, $s \geq 1$, and nodes $r$ in the orbit of the $0$ node in the Dynkin diagram. Our proof is almost uniform except we prove some technical lemmas by first proving the case when the $r$-th fundamental weight $Λ_r$ is minuscule by using properties of minuscule crystal and then extend this to the case when $Λ_r$ is cominuscule using virtual crystals.

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Il-Seung Jang, Travis Scrimshaw. 2026-08-28. Special Kirillov-Reshetikhin crystals. https://arxiv.org/abs/2608.27949

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