On the Arithmetic Exceptionality of Polynomial Mappings

TL;DR

This paper demonstrates that specific polynomial mappings derived from simple complex Lie algebras are exceptional, highlighting their unique arithmetic properties across multiple variables.

Contribution

It establishes the arithmetic exceptionality of polynomial mappings associated with simple complex Lie algebras for arbitrary rank.

Findings

Polynomial mappings from simple Lie algebras are exceptional.

The exceptionality holds for arbitrary rank n.

Provides a new perspective on the arithmetic properties of Lie algebra-derived polynomials.

Abstract

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.