On the Arithmetic Exceptionality of Polynomial Mappings

In this note we prove that certain polynomial mappings $P_{\mathfrak{g}}^k(\mathbf{x})\in \mathbf{Z}[\mathbf{x}]$ in $n$-variables obtained from simple complex Lie algebras $\mathfrak{g}$ of arbitrary rank $n \ge 1$, are exceptional.