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Representation Theory

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

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Splitting fields of real irreducible representations of finite groups
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by Dmitrii V. Pasechnik PDF
Represent. Theory 25 (2021), 897-902

Abstract:

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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Additional Information
  • Dmitrii V. Pasechnik
  • Affiliation: Department of Computer Science, University of Oxford, United Kingdom
  • MR Author ID: 292421
  • Email: dima@pasechnik.info
  • 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: https://doi.org/10.1090/ert/587
  • MathSciNet review: 4324950