Remarks concerning linear characters of reflection groups

Author:
G. I. Lehrer

Journal:
Proc. Amer. Math. Soc. **133** (2005), 3163-3169

MSC (2000):
Primary 20F55; Secondary 14G05, 20G40, 51F15

Published electronically:
May 2, 2005

MathSciNet review:
2160177

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite group generated by unitary reflections in a Hermitian space , and let be a root of unity. Let be a subspace of , maximal with respect to the property of being a -eigenspace of an element of , and let be the parabolic subgroup of elements fixing pointwise. If is any linear character of , we give a condition for the restriction of to to be trivial in terms of the invariant theory of , and give a formula for the polynomial , where is the dimension of the -eigenspace of . Applications include criteria for regularity, and new connections between the invariant theory and the structure of .

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Additional Information

**G. I. Lehrer**

Affiliation:
School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia

Email:
gusl@maths.usyd.edu.au

DOI:
http://dx.doi.org/10.1090/S0002-9939-05-07869-X

Received by editor(s):
December 12, 2003

Received by editor(s) in revised form:
June 8, 2004, and June 14, 2004

Published electronically:
May 2, 2005

Communicated by:
John R. Stembridge

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.