## *Branching Problems and Symmetry Breaking Operators*.
Geometry, Symmetry and Physics. Yale University, USA, 23 April 2019.

I begin with some new general results on restricting representations
of reductive groups to their subgroups.
Then I will focus on a concrete geometric question arising from
conformal geometry,
giving the complete classification of conformally covariant symmetry
breaking operators for differential forms on the model space for
codimension one submanifolds.
Some of the symmetry breaking operators are differential operators and
some others are obtained as the meromorphic continuation of integral
operators.

If time permits, I would like to discuss some applications and
related questions including a conjecture of Gross and Prasad.

References:

T. Kobayashi. A program for branching problems in the
representation theory of real reductive groups. Progr. Math. vol. 312,
pp. 277-322, 2015.

T. Kobayashi, T. Kubo, and M. Pevzner, Conformal symmetry
breaking operators for differential forms on spheres, viii+192 pages.
Lecture Notes in Mathematics, vol. 2170, 2016.

T. Kobayashi and B. Speh. Symmetry Breaking for Representations
of Rank One Orthogonal Groups, Memoirs of Amer. Math. Soc. 238. 2015.
118 pages.

T. Kobayashi and B. Speh, xv+342 pages, Lecture Notes in Math.
2234, Springer-Nature, 2018.

© Toshiyuki Kobayashi