Work

Special Kirillov-Reshetikhin crystals

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.27949

Authors: Jang, Il-Seung, Scrimshaw, Travis

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Research Foundation, Ministry of Education, Culture, Sports, Science and Technology, National Research Foundation of Korea, Ministry of Science and ICT, South Korea, Japan Society for the Promotion of Science

Awards: Institute for Computational and Experimental Research in Mathematics, G1600039682, G1681749534, Supersymmetry in the geometry of particle systems, Supersymmetric rigged configurations and crystals of quantum affine supergroups, Fixed points, random processes, and supersymmetry

OpenAlex ID: W7204766145

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