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.