We give a complete classification of the reductive symmetric pairs (G,H) for which the homogeneous space (G ×H)/diag H is real spherical in the sense that a minimal parabolic subgroup has an open orbit. Combining with a criterion established in [T. Kobayashi-T. Oshima, Adv. Math. 2013], we give a necessary and sufficient condition for a reductive symmetric pair (G,H) such that the multiplicities for the branching law of the restriction of any admissible smooth representation of G to H have finiteness/boundedness property.
© Toshiyuki Kobayashi