On some properties of polynomial mappings related to Lie algebras (Q1109862)

In [Sov. Math., Dokl. 35, 211-213 (1987); translation from Dokl. Akad. Nauk SSSR 292, 1289-1291 (1987; Zbl 0631.32024)] \textit{A. P. Veselov} defined a class of polynomial mappings \({\mathbb{C}}^ n\to {\mathbb{C}}^ n\) connected with simple complex Lie algebras. It was shown that except \(B_ n\) and \(C_ n\) the Lie algebras with nonisomorphic Weyl groups correspond to nonequivalent series of mappings. Here the author proves that series of maps for \(B_ n\) and \(C_ n\) are nonequivalent. Moreover polynomial mappings \({\mathbb{C}}P^ n\to {\mathbb{C}}P^ n\) are studied.