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Pré-Publication, Document De Travail Année : 2017

An asymptotic cell category for cyclic groups

Raphaël Rouquier
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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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Dates et versions

hal-01579429 , version 1 (31-08-2017)
hal-01579429 , version 2 (05-09-2017)
hal-01579429 , version 3 (17-10-2018)
hal-01579429 , version 4 (15-10-2019)

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Citer

Cédric Bonnafé, Raphaël Rouquier. An asymptotic cell category for cyclic groups. 2017. ⟨hal-01579429v1⟩
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