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Representations of complex imprimitive reflection groups

Published online by Cambridge University Press:  24 October 2008

M. C. Hughes
M. C. Hughes
Affiliation:
24 Marriners Lane, Allesley Park, Coventry CV5 9LD
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Extract

In his attempt to give the irreducible characters of the Weyl groups of type A, B and D, Mayer [3] found a unified theory using their common structure as reflection groups. In this paper, we give the characters of the complex imprimitive reflection groups. We are able to give an algorithm which allows us to calculate the irreducible components of the principal character of a ‘Weyl’ subgroup induced up to the whole group. This is a generalization of the algorithm given by Mayer.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 3 , November 1983 , pp. 425 - 436
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

[1] Cohen, A. M.. Complex reflection groups. Thesis, University of Utrecht (1976).CrossRefGoogle Scholar
[2] Hughes, M. C.. The representations of complex reflection groups. Thesis, University of Wales, 1981.Google Scholar
[3] Mayer, S. J.. On the irreducible characters of the Weyl groups. Thesis, University of Warwick, 1971.Google Scholar
[4] Read, E. W.. On the finite imprimitive unitary reflection groups. J. Algebra 45, no. 2 (1977), 439–452.CrossRefGoogle Scholar
[5] Serre, J. P.. Linear Representations of Finite Groups (Springer-Verlag, 1977).CrossRefGoogle Scholar