## 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,*H* ∩ *K*)-module.

We investigate further if such X can be taken to be a minimal representation,
a Zuckerman derived functor module *A*_{q}(λ), or some other unitarizable
(g,*K*)-module. The tensor product π_{1} ⊗ π_{2} of two infinite-dimensional irreducible
(g,*K*)-modules arises as a very special case of our setting. In this
case, we prove that π_{1} ⊗ π_{2} is discretely decomposable if and only if they are
simultaneously highest weight modules.

[ DOI |
arXiv |
preprint version(pdf) ]

© Toshiyuki Kobayashi