On the discretely decomposable restrictions of (𝔤,K)-modules for Klein four symmetric pairs

Abstract

We prove a criterion for Klein four symmetric pairs [Formula: see text] satisfying the condition that there exist infinite-dimensional simple [Formula: see text]-modules which are discretely decomposable as [Formula: see text]-modules. Making use of the criterion, we classify all the Klein four symmetric pairs satisfying the condition for the exceptional Lie groups of Hermitian type: [Formula: see text] and [Formula: see text].