Slightly degenerate categories and Z-modular data

Data

• Title: Slightly degenerate categories and $\mathbb{Z}$-modular data
• Authors: Abel Lacabanne
• arXiv link: https://arxiv.org/abs/1807.00766
• Published in: Int. Math. Res. Not. IMRN (2021), no. 12, 9340–9374.
• DOI: 10.1093/imrn/rnz105

Abstract

Given a slightly degenerate fusion category $\mathcal{C}$, we explain how it naturally gives rise to a $\mathbb{Z}$-modular data. We do not restrict to spherical categories and work with pivotal categories instead. Finally, we give an interpretation in this framework of the Bonnafé-Rouquier categorification of the $\mathbb{Z}$-modular datum associated to non trivial family of the cyclic complex reflection group.

Citation

@article {MR4276321,
    AUTHOR = {Lacabanne, Abel},
     TITLE = {Slightly degenerate categories and {$\Bbb{Z}$}-modular data},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2021},
    NUMBER = {12},
     PAGES = {9340--9374},
      ISSN = {1073-7928,1687-0247},
   MRCLASS = {18M20 (05E16 20F55)},
  MRNUMBER = {4276321},
MRREVIEWER = {Eric\ C.\ Rowell},
       DOI = {10.1093/imrn/rnz105},
       URL = {https://doi.org/10.1093/imrn/rnz105},
}