Separating invariants for the basic G_a-actions

TL;DR

This paper constructs a finite set of separating invariants for basic additive group actions, specifically for indecomposable rational linear representations over fields of characteristic zero, using the kernel of the Weitzenböck derivation.

Contribution

It explicitly constructs separating invariants for all indecomposable rational linear representations of the additive group in characteristic zero.

Findings

Finite set of separating invariants explicitly constructed.

Invariants are given by the kernel of the Weitzenböck derivation.

Applicable to all indecomposable rational linear representations.

Abstract

We explicitly construct a finite set of separating invariants for the basic $\Ga$-actions. These are the finite dimensional indecomposable rational linear representations of the additive group $\Ga$ of a field of characteristic zero, and their invariants are the kernel of the Weitzenb\"ock derivation $D_{n}=x_{0}\frac{\partial}{\partial{x_{1}}}+...+ x_{n-1}\frac{\partial}{\partial{x_{n}}}$.