Uniform construction and proof of Kirillov–Reshetikhin crystals

Provide a uniform construction and proof of the existence and crystal structure of Kirillov–Reshetikhin crystals across all affine types, extending beyond the special-node cases treated in the paper.

Background

Kirillov–Reshetikhin crystals B^{r,s} are combinatorial counterparts of Kirillov–Reshetikhin modules for affine quantum groups. Although these crystals have been intensively studied and their existence has been established in many individual cases, available realizations are often type-specific or depend on diagram automorphisms. The paper addresses this broader problem for special nodes, namely nodes in the orbit of the affine node 0, and gives a uniform PBW-crystal realization in that setting. A uniform construction and proof for KR crystals without this restriction remains unresolved.