Sur les distributions covariantes dans les alg\`ebres de Lie r\'eductives

TL;DR

This paper investigates whether covariant distributions on reductive Lie algebras can be expressed as finite sums of products involving invariant distributions and covariant polynomials.

Contribution

It introduces a method to factor covariant distributions on reductive Lie algebras, expanding understanding of their structure.

Findings

Covariant distributions can be factored as finite sums of invariant distributions times covariant polynomials.

The study provides conditions under which such factorizations are possible.

Results contribute to the theory of distributions on Lie algebras and their invariance properties.

Abstract

We study the possibility of factoring a covariant distribution on reductive Lie algebras as finite sum of products of an invariant distribution by a covariant polynomial.