## T. Kobayashi.
Bounded multiplicity theorems for induction and restriction.
Journal of Lie Theory
**32** (2022), 197-238, arXiv:
2109.14424.

We prove a geometric criterion
for the bounded multiplicity property
of “small”
infinite-dimensional representations
of real reductive Lie groups
in both induction and restrictions.
Applying the criterion to symmetric pairs,
we give a full description of the triples *H* ⊂ *G* ⊃ *G*'
such that any irreducible admissible representations of *G*
with *H*-distinguished vectors
have the bounded multiplicity property
when restricted to the subgroup *G*'.
This article also completes the proof of the general results
announced in the previous paper
[Adv. Math. 2021, Section 7].

[ arXiv |
preprint version(pdf) ]

© Toshiyuki Kobayashi