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Involutions and characters of upper triangular matrix groups


Authors: I. M. Isaacs and Dikran B. Karagueuzian
Journal: Math. Comp. 74 (2005), 2027-2033
MSC (2000): Primary 20C15; Secondary 20D15
DOI: https://doi.org/10.1090/S0025-5718-05-01705-9
Published electronically: March 24, 2005
MathSciNet review: 2164110
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the realizability over $\mathbb{R} $ of representations of the group $U(n)$ of upper-triangular $n \times n$ matrices over $\mathbb{F} _2$. We prove that all the representations of $U(n)$ are realizable over $\mathbb R$ if $n \leq 12$, but that if $n \geq 13$, $U(n)$ has representations not realizable over $\mathbb R$. This theorem is a variation on a result that can be obtained by combining work of J. Arregi and A. Vera-López and of the authors, but the proof of the theorem in this paper is much more natural.


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Additional Information

I. M. Isaacs
Affiliation: Mathematics Department, University of Wisconsin at Madison, Madison, Wisconsin 53706
Email: isaacs@math.wisc.edu

Dikran B. Karagueuzian
Affiliation: Mathematics Department, Binghamton University, Binghamton, New York, 13902-6000
Email: dikran@math.binghamton.edu

DOI: https://doi.org/10.1090/S0025-5718-05-01705-9
Keywords: Character theory, finite groups, p-groups
Received by editor(s): August 6, 2002
Received by editor(s) in revised form: February 24, 2004
Published electronically: March 24, 2005
Additional Notes: The research of the second author was partially supported by an N.S.F. Postdoctoral Fellowship, the MPIM-Bonn, and the CRM-Barcelona.
Article copyright: © Copyright 2005 American Mathematical Society

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