We give a complete classification
of reductive symmetric pairs
with the following property:
there exists at least one infinite-dimensional irreducible (𝔤,K)-module X
that is discretely decomposable
as an -module.
We investigate further if such X can be taken to be a minimal representation,
a Zuckerman derived functor module ,
or some other unitarizable (𝔤,K)-module.
The tensor product
of two infinite-dimensional irreducible (𝔤,K)-modules
arises as a very special case
of our setting.
In this case, we prove that
is discretely decomposable if and only if π1 and π2 are simultaneously highest weight modules.