Data
- Title: Fourier matrices for $G(d,1,n)$ from quantum general linear groups
- Authors: Abel Lacabanne
- arXiv link: https://arxiv.org/abs/2011.11332
- Published in: J. Algebra 586 (2021), 433–466.
- DOI: 10.1016/j.jalgebra.2021.06.034
Abstract
We construct a categorification of the modular data associated with every family of unipotent characters of the spetsial complex reflection group $G(d,1,n)$. The construction of the category follows the decomposition of the Fourier matrix as a Kronecker tensor product of exterior powers of the character table $S$ of the cyclic group of order $d$. The representation of the quantum universal enveloping algebra of the general linear Lie algebra $\mathfrak{gl}_{m}$, with quantum parameter an even root of unity of order $2d$, provides a categorical interpretation of the matrix $\bigwedge^m S$. We also prove some positivity conjectures of Cuntz at the decategorified level.
Citation
@article {MR4291489,
AUTHOR = {Lacabanne, Abel},
TITLE = {Fourier matrices for {$G( d,1, n)$} from quantum general
linear groups},
JOURNAL = {J. Algebra},
FJOURNAL = {Journal of Algebra},
VOLUME = {586},
YEAR = {2021},
PAGES = {433--466},
ISSN = {0021-8693,1090-266X},
MRCLASS = {20G42 (18M05 20F55 20G05)},
MRNUMBER = {4291489},
MRREVIEWER = {Thorsten\ Heidersdorf},
DOI = {10.1016/j.jalgebra.2021.06.034},
URL = {https://doi.org/10.1016/j.jalgebra.2021.06.034},
}