Summary: Some Applications of Plurisubharmonic Functions to Orbits of
Real Reductive Groups
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
Department de Mathematiques, Universit´e D'Angers, 49045 Angers, France
The principal aim of this paper is to prove the following results. Section 1 explains
the terminology involved; applications are given in Section 4.
Theorem 1. Let G GL(n, R) be a real reductive group with Cartan decomposition
g = k p, g being the Lie algebra of G.
be the subgroup of GL(n, C) with Lie algebra g ig and ~K the subgroup of GC
whose Lie algebra is k ip.
be a complex homogeneous space for GC
and a ~K-invariant strictly plurisub-
harmonic function on C