Splitting fields of real irreducible representations of finite groups

Pasechnik, Dmitrii

doi:10.1090/ert/587

Splitting fields of real irreducible representations of finite groups
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by Dmitrii V. Pasechnik

Represent. Theory 25 (2021), 897-902

DOI: https://doi.org/10.1090/ert/587

Published electronically: October 14, 2021

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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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