Linear locally nilpotent derivations and the classical invariant theory, I: The Poincare series

TL;DR

This paper presents formulas derived from classical invariant theory to compute the Poincare series of the kernel of linear locally nilpotent derivations, advancing understanding in algebraic invariant theory.

Contribution

It introduces a new method using classical invariant theory to explicitly calculate the Poincare series for kernels of specific derivations.

Findings

Formulas for Poincare series are derived

The approach simplifies calculations in invariant theory

Results connect derivations with classical invariants

Abstract

By using classical invariant theory approach a formulas for computation of the Poincare series of the kernel of linear locally nilpotent derivations is found.