T. Kobayashi and Y. Oshima, Classification of symmetric pairs with discretely decomposable restrictions of (g,K)-modules, Journal für die reine und angewandte Mathematik (Crelles Journal) 2015 (2015), no. 703, 201-223, published online 2013 July 13. arXiv: 1202.5743. DOI: 10.1515/crelle-2013-0045..

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

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