Splitting fields of real irreducible representations of finite groups

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 $E$.

pdflatex/lualatex, 8 pages - accepted to AMS Representation Theory version

Cited by in corpus (1)

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