On some subspaces of the exterior algebra of a simple Lie algebra

TL;DR

This paper investigates specific subspaces within the exterior algebra of a simple Lie algebra, demonstrating that certain graded subspaces generate the entire module for particular degrees.

Contribution

It identifies conditions under which graded subspaces of the exterior algebra generate the Lie algebra modules, advancing understanding of their structure.

Findings

Certain graded subspaces generate the g-module d(g) for specific degrees

The paper provides new insights into the structure of subspaces in the exterior algebra

Results contribute to the representation theory of simple Lie algebras

Abstract

In this article, we are interested in some subspaces of the exterior algebra of a simple Lie algebra g. In particular, we prove that some graded subspaces of degree d generate the g-module d (g) for some integers d.