Polynomial invariants of Euclidean Lie algebras (Q1057975)

Let \(\Delta\) be a Euclidean (affine) root system of rank \(\ell\), W the Weyl group of \(\Delta\) and V the \({\mathbb{R}}\)-span of \(\Delta\). Denote the symmetric algebra of V resp. \(V^*\) (the dual of V) by \(S(V^*)\) resp. S(V). The author proves that the ring of W-invariants of S(V) is generated by \(\ell\) algebraically independent homogeneous polynomials (as in classical theory) and that the ring of W-invariants of \(S(V^*)\) is generated by a single element of V, namely a null root, i.e. a generating element of the set of imaginary roots, which is a free \({\mathbb{Z}}\)-module of rank one.