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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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.


Splitting fields of real irreducible representations of finite groups
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by Dmitrii V. Pasechnik
Represent. Theory 25 (2021), 897-902
Published electronically: October 14, 2021


We show that any irreducible representation $\rho$ of a finite group $G$ of exponent $n$, realisable over $\mathbb {R}$, is realisable over the field $E≔\mathbb {Q}(\zeta _n)\cap \mathbb {R}$ of real cyclotomic numbers of order $n$, and describe an algorithmic procedure transforming a realisation of $\rho$ over $\mathbb {Q}(\zeta _n)$ to one over $E$.
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Bibliographic Information
  • Dmitrii V. Pasechnik
  • Affiliation: Department of Computer Science, University of Oxford, United Kingdom
  • MR Author ID: 292421
  • Email:
  • Received by editor(s): July 13, 2021
  • Received by editor(s) in revised form: July 15, 2021
  • Published electronically: October 14, 2021
  • © Copyright 2021 Dmitrii V. Pasechnik
  • Journal: Represent. Theory 25 (2021), 897-902
  • MSC (2020): Primary 20C15, 20-08
  • DOI:
  • MathSciNet review: 4324950