zbMATH — the first resource for mathematics

Writing representations over minimal fields. (English) Zbl 0888.20013
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 \(O([E:F]d^3)\).

20C40 Computational methods (representations of groups) (MSC2010)
Full Text: DOI arXiv
[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.