Invariant plurisubharmonic functions on non-compact Hermitian symmetric spaces

Abstract

Let G/K be an irreducible Hermitian symmetric space and let D be a K-invariant domain in G/K. In this paper we characterize several classes of K-invariant plurisubharmonic functions on D in terms of their restrictions to a slice intersecting all K-orbits. As applications we show that K-invariant plurisubharmonic functions on D are necessarily continuous and we reproduce the classification of Stein K-invariant domains in G/K obtained by E. Bedford and J. Dadok.