Diagonalization in compact Lie algebras and a new proof of a theorem of Kostant

Abstract

We exhibit a simple algorithmic procedure to show that any element of a compact Lie algebra is conjugate to an element of a fixed maximal abelian subalgebra. An estimate of the convergence of the algorithm is obtained. As an application, we provide a new proof of Kostant’s theorem on the projection of orbits onto a maximal abelian subalgebra.