On the algebraic set of singular elements in a complex simple Lie algebra

Bertram Kostant, Nolan Wallach

Let $G$ be a complex simple Lie group and let $\g = \hbox{\rm Lie}\,G$. Let $S(\g)$ be the $G$-module of polynomial functions on $\g$ and let $\hbox{\rm Sing}\,\g$ be the closed al…