On Some Subspaces of the Exterior Algebra of a Simple Lie Algebra

Abstract

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