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

  • Abel Lacabanne

    Université Catholique de Louvain, Louvain-la-Neuve, Belgium
Drinfeld double of quantum groups, tilting modules, and $\mathbb Z$-modular data associated to complex reflection groups cover
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Abstract

Generalizing Lusztig’s work, Malle has associated to some imprimitive complex reflection group a set of “unipotent characters”, which are in bijection of the usual unipotent characters of the associated finite reductive group if is a Weyl group. He also obtained a partition of these characters into families and associated to each family a -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. As an application, we obtain a proof of a conjecture by Cuntz at the decategorified level.

Cite this article

Abel Lacabanne, Drinfeld double of quantum groups, tilting modules, and -modular data associated to complex reflection groups. J. Comb. Algebra 4 (2020), no. 3, pp. 269–323

DOI 10.4171/JCA/45