Involutions and characters of upper triangular matrix groups

Isaacs, I.; Karagueuzian, Dikran

doi:10.1090/S0025-5718-05-01705-9

Involutions and characters of upper triangular matrix groups
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by I. M. Isaacs and Dikran B. Karagueuzian;

Math. Comp. 74 (2005), 2027-2033

DOI: https://doi.org/10.1090/S0025-5718-05-01705-9

Published electronically: March 24, 2005

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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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