 
Summary: Some Applications of Plurisubharmonic Functions to Orbits of
Real Reductive Groups
H. Azad
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
and
J.J. Loeb
Department de Mathematiques, Universit´e D'Angers, 49045 Angers, France
INTRODUCTION
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.
Let GC
be the subgroup of GL(n, C) with Lie algebra g ig and ~K the subgroup of GC
whose Lie algebra is k ip.
Let C
be a complex homogeneous space for GC
and a ~Kinvariant strictly plurisub
harmonic function on C
