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Categorifications of noncrossing partitions of type B and affine type A

  • Yiyu Cheng
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Abstract

The lattice of wide subcategories of a tube is isomorphic to the lattice of noncrossing partitions of type B. We prove that through this categorification of noncrossing partitions, Kreweras complement is taking left perpendicular categories. With the help of this categorification and weighted projective lines, we obtain an inclusion from the lattice of noncrossing partitions of type B_n to a lattice of affine type A_n which preserves Kreweras complement.

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Cite

BibTeXRIS
BibTeX
@misc{cheng2026categorifications,
  title = {{Categorifications of noncrossing partitions of type B and affine type A}},
  author = {Yiyu Cheng},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00966},
  eprint = {2611.00966},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00966},
}
RIS
TY  - UNPB
TI  - Categorifications of noncrossing partitions of type B and affine type A
AU  - Yiyu Cheng
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00966
UR  - https://arxiv.org/abs/2611.00966
AB  - The lattice of wide subcategories of a tube is isomorphic to the lattice of noncrossing partitions of type B. We prove that through this categorification of noncrossing partitions, Kreweras complement is taking left perpendicular categories. With the help of this categorification and weighted projective lines, we obtain an inclusion from the lattice of noncrossing partitions of type B_n to a lattice of affine type A_n which preserves Kreweras complement.
ER  -