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The fields of values of characters of degree not divisible by p

Part of: Representation theory of groups

Published online by Cambridge University Press:  15 February 2021

Gabriel Navarro  and
Pham Huu Tiep
Gabriel Navarro
Affiliation:
Department of Mathematics, Universitat de València, València, Spain; E-mail: gabriel@uv.es
Pham Huu Tiep
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ, USA; E-mail: tiep@math.rutgers.edu

Abstract

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We study the fields of values of the irreducible characters of a finite group of degree not divisible by a prime p. In the case where $p=2$, we fully characterise these fields. In order to accomplish this, we generalise the main result of [ILNT] to higher irrationalities. We do the same for odd primes, except that in this case the analogous results hold modulo a simple-to-state conjecture on the character values of quasi-simple groups.

MSC classification

Primary: 20C15: Ordinary representations and characters 20C33: Representations of finite groups of Lie type
Type
Algebra
Information
Forum of Mathematics, Pi , Volume 9 , 2021 , e2
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

Dedicated to Gunter Malle on the occasion of his 60th birthday

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