Brauer and iquantum categorification

Abstract

We show that locally finite Abelian module categories over the affine Brauer category are the same thing as locally finite Abelian 2-representations of a certain 2-iquantum group satisfying some additional nilpotency and finiteness properties. Our results are valid over algebraically closed fields of characteristic other than 2 and for arbitrary spectra. This extends recent work of Gao, Rui and Song, who treated characteristic 0 with half-integral spectrum. The relevant Satake diagrams are of quasi-split type AIII and of diagonal type A, including affine types in positive characteristic. The key step in our approach identifies the affine Brauer category with a topologically dense monoidal subcategory of a completion of the 2-iquantum group. As an application, we show that deformed cyclotomic quotients on the two sides are equivalent.

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BibTeX RIS

BibTeX

@misc{brundan2026brauer,
  title = {{Brauer and iquantum categorification}},
  author = {Jonathan Brundan and Alistair Savage and Ben Webster},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25922},
  eprint = {2610.25922},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25922},
}

RIS

TY  - UNPB
TI  - Brauer and iquantum categorification
AU  - Jonathan Brundan
AU  - Alistair Savage
AU  - Ben Webster
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.25922
UR  - https://arxiv.org/abs/2610.25922
AB  - We show that locally finite Abelian module categories over the affine Brauer category are the same thing as locally finite Abelian 2-representations of a certain 2-iquantum group satisfying some additional nilpotency and finiteness properties. Our results are valid over algebraically closed fields of characteristic other than 2 and for arbitrary spectra. This extends recent work of Gao, Rui and Song, who treated characteristic 0 with half-integral spectrum. The relevant Satake diagrams are of quasi-split type AIII and of diagonal type A, including affine types in positive characteristic. The key step in our approach identifies the affine Brauer category with a topologically dense monoidal subcategory of a completion of the 2-iquantum group. As an application, we show that deformed cyclotomic quotients on the two sides are equivalent.
ER  -

Abstract

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