## T. Kobayashi.
Recent advances in branching problems of representations.
To appear in Sugaku Expositions, Amer. Math. Soc.; a translation by
Toshihisa Kubo of the Japanese original article.
arXiv: 2112.00642.

How does an irreducible representation of a group
behave when restricted to a subgroup?
This is part of *branching problems*,
which are one of the fundamental problems in representation theory,
and also interact naturally with other fields of mathematics.
This expository paper is an up-to-date account on some new directions in
representation theory highlighting the branching problems for real
reductive groups and their related topics ranging from global analysis
of manifolds via group actions to the theory of discontinuous groups
beyond the classical Riemannian setting.

This article is an outgrowth of the invited lecture that
the author delivered at the commemorative event for
the 70th anniversary of the re-establishment
of the Mathematical Society of Japan,
and originally appeared in Japanese in Sugaku **71** (2019).

[ arXiv |
preprint version(pdf) ]

© Toshiyuki Kobayashi