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PreprintCC BY 4.0arXiv

Big categorification on towers of classical groups and wreath product groups

  • Xin Huang
  • Pengcheng Li
  • Yaolong Shen
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Abstract

We develop a uniform framework for ``big'' categorification of representation categories of towers of finite classical groups and wreath product groups. We construct actions of symmetric products of Heisenberg categories, quantum in the finite classical group case and degenerate in the wreath product case. These actions lead to categorical actions of suitable symmetric products of Kac--Moody 2-categories, and hence to actions of large Lie algebras on Grothendieck groups. In characteristic zero, the resulting actions control the full graded centers of the group algebras through diagrammatic central elements, and the associated colored weight functions separate all irreducible ordinary characters. We also obtain modular block descriptions for wreath product groups through categorification.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026categorification,
  title = {{Big categorification on towers of classical groups and wreath product groups}},
  author = {Xin Huang and Pengcheng Li and Yaolong Shen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.17709},
  eprint = {2608.17709},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.17709},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Big categorification on towers of classical groups and wreath product groups
AU  - Xin Huang
AU  - Pengcheng Li
AU  - Yaolong Shen
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2608.17709
UR  - https://arxiv.org/abs/2608.17709
AB  - We develop a uniform framework for ``big'' categorification of representation categories of towers of finite classical groups and wreath product groups. We construct actions of symmetric products of Heisenberg categories, quantum in the finite classical group case and degenerate in the wreath product case. These actions lead to categorical actions of suitable symmetric products of Kac--Moody 2-categories, and hence to actions of large Lie algebras on Grothendieck groups. In characteristic zero, the resulting actions control the full graded centers of the group algebras through diagrammatic central elements, and the associated colored weight functions separate all irreducible ordinary characters. We also obtain modular block descriptions for wreath product groups through categorification.
ER  -