## T. Kobayashi, *Global analysis by hidden symmetry*,
Representation Theory,
Number Theory, and Invariant Theory: In Honor of Roger Howe on the
Occasion of His 70th Birthday (Jim Cogdell, Ju-Lee Kim, and Chen-Bo Zhu,
eds.), Progress in Mathematics, vol. 323 (2017), pp. 359-397.
DOI: 10.1007/978-3-319-59728-7_13.
arXiv: 160808356. ISBN
978-3-319-59727-0..

Hidden symmetry of a *G*'-space *X* is defined by an extension
of the *G*'-action on *X* to that of a group *G* containing *G*'
as a subgroup.
In this setting,
we study the relationship
between the three objects:
(A) global analysis on *X*
by using representations of *G* (hidden symmetry);

(B) global analysis on *X*
by using representations of *G*';

(C) branching laws of representations
of *G*
when restricted to the subgroup *G*'.

We explain a trick
which transfers results
for finite-dimensional representations
in the compact setting
to those for infinite-dimensional representations
in the noncompact setting
when *X*_{C} is *G*'_{C}-spherical.
Applications to branching problems
of unitary representations,
and to spectral analysis on pseudo-Riemannian locally symmetric spaces
are also discussed.

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© Toshiyuki Kobayashi