Drinfeld double of quantum groups, tilting modules and Z-modular data associated to complex reflection groups

Data

• Title: Drinfeld double of quantum groups, tilting modules and $\mathbb{Z}$-modular data associated to complex reflection groups
• Authors: Abel Lacabanne
• arXiv link: https://arxiv.org/abs/1807.00770
• Published in: J. Comb. Algebra 4 (2020), no.3, 269-323.
• DOI: 10.4171/JCA/45

Abstract

Generalizing Lusztig’s work, Malle has associated to some imprimitive complex reflection group $W$ a set of "unipotent characters", which are in bijection of the usual unipotent characters of the associated finite reductive group if $W$ is a Weyl group. He also obtained a partition of these characters into families and associated to each family a $\mathbb{Z}$-modular datum. We construct a categorification of some of these data, by studying the category of tilting modules of the Drinfeld double of the quantum enveloping algebra of the Borel of a simple complex Lie algebra.

Citation

@article {MR4162292,
    AUTHOR = {Lacabanne, Abel},
     TITLE = {Drinfeld double of quantum groups, tilting modules, and {$\Bbb
              Z$}-modular data associated to complex reflection groups},
   JOURNAL = {J. Comb. Algebra},
  FJOURNAL = {Journal of Combinatorial Algebra},
    VOLUME = {4},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {269--323},
      ISSN = {2415-6302,2415-6310},
   MRCLASS = {20G42 (18M15 20F55)},
  MRNUMBER = {4162292},
MRREVIEWER = {Iulian\ Ion\ Simion},
       DOI = {10.4171/JCA/45},
       URL = {https://doi.org/10.4171/JCA/45},
}