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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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On the generic degrees of cyclotomic algebras
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by Gunter Malle PDF
Represent. Theory 4 (2000), 342-369 Request permission


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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Additional Information
  • Gunter Malle
  • Affiliation: FB Mathematik/Informatik, Universität Kassel, Heinrich-Plett-Str. 40, D–34132 Kassel, Germany
  • MR Author ID: 225462
  • Email:
  • 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
  • © Copyright 2000 American Mathematical Society
  • Journal: Represent. Theory 4 (2000), 342-369
  • MSC (2000): Primary 20C08, 20C40
  • DOI:
  • MathSciNet review: 1773866