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Involutions and characters of upper triangular matrix groups

Authors:	I M Isaacs Dikran B Karagueuzian

Institution:	Mathematics Department, University of Wisconsin at Madison, Madison, Wisconsin 53706 ; Mathematics Department, Binghamton University, Binghamton, New York, 13902-6000

Abstract:	We study the realizability over $\mathbb{R}$ of representations of the group of upper-triangular $n \times n$ matrices over $\mathbb{F} _2$ . We prove that all the representations of are realizable over $\mathbb R$ if $n \leq 12$ , but that if $n \geq 13$ , 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.

Keywords:	Character theory finite groups p-groups

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