The field of invariants of the adjoint action of the unitriangular group in the nilradical of a parabolic subalgebra

TL;DR

This paper characterizes the field of invariants under the adjoint action of the unitriangular group on the nilradical of parabolic subalgebras, providing a comprehensive description of these invariants.

Contribution

It offers a complete description of the invariants for the adjoint action on the nilradical of any parabolic subalgebra, extending previous understanding in this area.

Findings

Explicit description of the invariant field for all parabolic subalgebras.

Generalization of known results from specific cases to all parabolic subalgebras.

Foundation for further algebraic and geometric analysis of invariants.

Abstract

In the present paper the field of invariants of the adjoint action of the unitriangular group in the nilradical of any parabolic subalgebra is described.