## Abstract

We give a complete classification
of reductive symmetric pairs $(\mathrm{\u0111\x9d\x94\u20ac},\mathrm{\u0111\x9d\x94\u201e})$
with the following property:
there exists at least one infinite-dimensional irreducible (đ€,*K*)-module *X*
that is discretely decomposable
as an $(\mathrm{\u0111\x9d\x94\u201e},H\xe2\x88\copyright K)$-module.
We investigate further if such *X* can be taken to be a minimal representation,
a Zuckerman derived functor module ${A}_{\mathrm{\u0111\x9d\x94\u017a}}\left(\mathrm{\xce\xbb}\right)$,
or some other unitarizable (đ€,*K*)-module.
The tensor product ${\mathrm{\xcf\x80}}_{1}\xe2\x8a\x97{\mathrm{\xcf\x80}}_{2}$
of two infinite-dimensional irreducible (đ€,*K*)-modules
arises as a very special case
of our setting.
In this case, we prove that ${\mathrm{\xcf\x80}}_{1}\xe2\x8a\x97{\mathrm{\xcf\x80}}_{2}$
is discretely decomposable if and only if Ï_{1} and Ï_{2} are simultaneously highest weight modules.

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