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Constructing representations of Hecke algebras for complex reflection groups

Part of: Representation theory of groups Computational aspects of associative rings

Published online by Cambridge University Press:  01 August 2010

Gunter Malle  and
Jean Michel
Gunter Malle
Affiliation:
FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany (email: malle@mathematik.uni-kl.de)
Jean Michel
Affiliation:
CNRS, Université Paris VII, 175, rue du Chevaleret, 75013 Paris, France (email: jmichel@math.jussieu.fr)

Abstract

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We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras, including a generalization of the concept of aW-graph to the situation of complex reflection groups. We then use these techniques to find models for all irreducible representations in the case of complex reflection groups of dimension at most three. Using these models we are able to verify some important conjectures on the structure of Hecke algebras.

MSC classification

Secondary: 16Z05: Computational aspects of associative rings 20C08: Hecke algebras and their representations
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 13 , January 2010 , pp. 426 - 450
Copyright
Copyright © London Mathematical Society 2010

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