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The Weil-Steinberg character of finite classical groups


Authors: G. Hiss and A. Zalesski; \\ with an appendix by Olivier Brunat
Journal: Represent. Theory 13 (2009), 427-459
MSC (2000): Primary 20G40, 20C33
DOI: https://doi.org/10.1090/S1088-4165-09-00351-3
Published electronically: September 24, 2009
Corrigendum: Represent. Theory 15 (2011), 729-732.
MathSciNet review: 2550472
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $G$ be one of the groups $\operatorname {GL}(n,q)$ or $U(n,q)$, and let $H$ denote the subgroup $\operatorname {GL}({n-1},q)$ or $U(n-1,q)$, respectively. We show that the restriction of the Steinberg character of $G$ to $H$ equals the product of the Weil character and the Steinberg character of $H$.


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Additional Information

G. Hiss
Affiliation: Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen, Germany
MR Author ID: 86475
Email: gerhard.hiss@math.rwth-aachen.de

A. Zalesski
Affiliation: School of Mathematics, University of East Anglia, Norwich, NR47TJ, United Kingdom
MR Author ID: 196858
Email: alexandre.zalesski@gmail.com

Olivier Brunat
Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum
Email: olivier.brunat@ruhr-uni-bochum.de

Keywords: Weil character, Steinberg character, classical groups
Received by editor(s): September 26, 2007
Received by editor(s) in revised form: June 14, 2008
Published electronically: September 24, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.