Invariant fields of finite irreducible reflection groups
The main result of this paper is a proof that if \(G\) is a finite irreducible reflection group over a field \(k\), then the invariant field of \(G\) is purely transcendental over \(k\), even when \(|G|\) is divisible by the characteristic of \(k\). An essential ingredient of the proof is the use of a package for the invariant theory of finite groups in the computer algebra system Magma.
scientific article; zbMATH DE number 1395778