On the generic degrees of cyclotomic algebras

Malle, Gunter

doi:10.1090/S1088-4165-00-00088-1

On the generic degrees of cyclotomic algebras
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by Gunter Malle

Represent. Theory 4 (2000), 342-369

DOI: https://doi.org/10.1090/S1088-4165-00-00088-1

Published electronically: August 1, 2000

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Abstract:

We determine the generic degrees of cyclotomic Hecke algebras attached to exceptional finite complex reflection groups. The results are used to introduce the notion of spetsial reflection group, which in a certain sense is a generalization of the finite Weyl group. In particular, to spetsial $W$ there is attached a set of unipotent degrees which in the case of a Weyl group is just the set of degrees of unipotent characters of finite reductive groups with Weyl group $W$, and in general enjoys many of their combinatorial properties.

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