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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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:
  • Dikran B. Karagueuzian
  • Affiliation: Mathematics Department, Binghamton University, Binghamton, New York, 13902-6000
  • Email:
  • 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:
  • MathSciNet review: 2164110