An asymptotic cell category for cyclic groups
Résumé
Gunter Malle has associated to any spetsial imprimitive complex reflection group $W$ a set of unipotent characters (which is in natural bijection with the set of unipotent characters of the associated finite reductive group whenever $W$ is a Weyl group). In this generalization of Lusztig's work, he also obtained a partition of this set into families and, to each family, he associated a $Z$-fusion datum. The aim of this paper is to provide an ad hoc categorification of the $Z$-fusion datum associated with the non-trivial family of the cyclic complex reflection group of order $d$ : it is provided by the stable category of the Drinfeld double of the Taft algebra of dimension $d²$.
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