Glasby, S. P.; Howlett, R. B. Writing representations over minimal fields. (English) Zbl 0888.20013 Commun. Algebra 25, No. 6, 1703-1711 (1997). The paper describes a procedure which determines whether an absolutely irreducible representation \(\rho\colon G\to\text{GL}(d,E)\) of a finite group \(G\) over a finite field \(E\) is equivalent to a representation \(G\to\text{GL}(d,F)\), where \(F\) is a subfield of \(E\). If so, the algorithm produces an \(A\in\text{GL}(d,E)\) such that \(A^{-1}\rho(g)A\in\text{GL}(d,F)\) for each \(g\in G\). The algorithm relies on a matrix version of Hilbert’s Theorem 90 and is probabilistic with expected running time \(O([E:F]d^3)\). Reviewer: K.-H.Zimmermann (Hamburg) Cited in 16 Documents MSC: 20C40 Computational methods (representations of groups) (MSC2010) Keywords:matrix representations; probabilistic algorithms; absolutely irreducible representations; finite groups; matrix version of Hilbert’s Theorem 90 PDF BibTeX XML Cite \textit{S. P. Glasby} and \textit{R. B. Howlett}, Commun. Algebra 25, No. 6, 1703--1711 (1997; Zbl 0888.20013) Full Text: DOI arXiv References: [1] DOI: 10.1017/S1446788700036016 · doi:10.1017/S1446788700036016 [2] Huppert B., Finite Groups II (1982) · Zbl 0477.20001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.