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Representation Theory

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On the generic degrees of cyclotomic algebras

Author: Gunter Malle
Journal: Represent. Theory 4 (2000), 342-369
MSC (2000): Primary 20C08, 20C40
Published electronically: August 1, 2000
MathSciNet review: 1773866
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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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Gunter Malle
Affiliation: FB Mathematik/Informatik, Universität Kassel, Heinrich-Plett-Str. 40, D–34132 Kassel, Germany

Received by editor(s): October 28, 1999
Received by editor(s) in revised form: June 19, 2000
Published electronically: August 1, 2000
Additional Notes: I’m grateful to J. Michel for spotting some inaccuracies in an earlier version of this paper.
I thank the Science University of Tokyo for its hospitality and the Deutsche Forschungsgemeinschaft for financial support
Article copyright: © Copyright 2000 American Mathematical Society