## T. Kobayashi and T. Matsuki.
Classification of finite-multiplicity symmetric pairs.
Transformation Groups **19** (2014), 457-493, Special Issue in honour of Professor Dynkin for his 90th birthday.
DOI: 10.1007/s00031-014-9265-x. arXiv: 1312.4246..

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.

[ DOI |
arXiv |
preprint version(pdf) ]

© Toshiyuki Kobayashi