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PreprintCC BY 4.0arXiv

Special Kirillov-Reshetikhin crystals

  • Il-Seung Jang
  • Travis Scrimshaw
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Abstract

We give a uniform realization of Kirillov-Reshetikhin crystals Br,s, in terms of PBW crystals, for all affine types, s ≥ 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 Λr is minuscule by using properties of minuscule crystal and then extend this to the case when Λr is cominuscule using virtual crystals.

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Cite

BibTeXRIS
BibTeX
@misc{jang2026special,
  title = {{Special Kirillov-Reshetikhin crystals}},
  author = {Il-Seung Jang and Travis Scrimshaw},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.27949},
  eprint = {2608.27949},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.27949},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Special Kirillov-Reshetikhin crystals
AU  - Il-Seung Jang
AU  - Travis Scrimshaw
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.27949
UR  - https://arxiv.org/abs/2608.27949
AB  - We give a uniform realization of Kirillov-Reshetikhin crystals B^r,s, in terms of PBW crystals, for all affine types, s ≥ 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.
ER  -