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

摘要

We give a method of determining the centralizer of an elliptic element in a real semisimple Lie algebra g, in relation with the maximal compact subalgebra of g and the compact dual of 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.