Admissible representations, multiplicity-free representations and visible actions on non-tube type Hermitian symmetric spaces

Abstract

This paper presents new characterization for a non-compact Hermitian symmetric space $G/K$ to be of tube type (or non-tube type) by multiplicities in some branching laws and visible actions. The study in this paper gives an example of a kind of the Cartan decomposition for non-symmetric homogeneous spaces.