Drinfeld double of quantum groups, tilting modules and $\mathbb Z$-modular data associated to complex reflection groups
(2020) Journal of Combinatorial Algebra — Vol. 4, n° 3, p. 269-323 (2020)
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- 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 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. As an application, we obtain a proof of a conjecture by Cuntz at the decategorified level.
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Citations
Lacabanne, A. (2020). Drinfeld double of quantum groups, tilting modules and $\mathbb Z$-modular data associated to complex reflection groups. Journal of Combinatorial Algebra, 4(3), 269-323. https://doi.org/10.4171/jca/45 (Original work published 2020)