On the invariant theory of finite pseudo reflection groups
The author gives a short noncomputational proof of a result of \textit{G. C. Shephard} and \textit{J. A. Todd} [Can. J. Math. 6, 274--304 (1954; Zbl 0055.14305)] and of \textit{C. Chevalley} [Am. J. Math. 77, 778--782 (1955; Zbl 0065.26103)]: \(G\leq \mathrm{GL}(V)\) is a finite group generated by pseudo reflections, where \(V\) is a vector space over the field \(k\), and assume \(\mathrm{char}\,k\nmid | G|\). Extend the action of \(G\) to the polynomial algebra on the vector space \(V\). Then the subring of invariant polynomials is isomorphic to a polynomial algebra.
finite group generated by pseudo reflections
scientific article; zbMATH DE number 3920792