On some subvarieties of the cartesian powers of a semisimple algebra related to a parabolic subalgebra

TL;DR

This paper explores desingularizations of specific subvarieties within cartesian powers of semisimple Lie algebras, providing insights into their geometric structure and singularities.

Contribution

It introduces new methods for desingularizing subvarieties associated with parabolic subalgebras in semisimple Lie algebras.

Findings

Describes explicit desingularizations of certain subvarieties.

Provides geometric insights into the structure of these subvarieties.

Contributes to the understanding of singularities in Lie algebra varieties.

Abstract

In this note, we describe some desingularizations of some subvarieties of the cartesian powers of a semisimple Lie algebra of finite dimension.