Isotropy subalgebras of elliptic orbits in semisimple Lie algebras, and the canonical representatives of pseudo-Hermitian symmetric elliptic orbits

Abstract

We give a method of determining the centralizer of an elliptic element in a real semisimple Lie algebra $\mathfrak{g}$, in relation with the maximal compact subalgebra of $\mathfrak{g}$ and the compact dual of $\mathfrak{g}$. Moreover, we determine a special central element (called the $H$-element) of the isotropy subalgebra of each simple irreducible pseudo-Hermitian symmetric Lie algebra.