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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Involutions and characters of upper triangular matrix groups
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by I. M. Isaacs and Dikran B. Karagueuzian PDF
Math. Comp. 74 (2005), 2027-2033 Request permission

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
  • 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.
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 2027-2033
  • MSC (2000): Primary 20C15; Secondary 20D15
  • DOI: https://doi.org/10.1090/S0025-5718-05-01705-9
  • MathSciNet review: 2164110