## *A Program for Branching Problems in the Representation Theory of
Real Reductive Groups: Classification Problem of Symmetry Breaking
Operators*.
Representation Theory inspired by the Langlands Conjectures
(organized by B. Speh and P. Trapa), in connection with the AMS-AWM Noether
lecture by Birgit Speh. Denver, USA, 17 January 2020.

A symmetry breaking operator is an intertwining operator that
arises from branching
problems of representations, thatis, an $H$-intertwining operator from an
(irreducible) representation of $G$
to that of the subgroup $H$. It may be an integraloperator,
and may be a more singular one such as a differential operator,
when representations are realized geometrically.
In general, it is a hard problem to classify symmetry breaking
operators.
We plan to discuss a criterion for the spaceof symmetry breaking
operators to be finite-dimensional,
and a classification scheme of symmetry breaking operatorswith
some examples for orthogonal groups.

References:

- T. Kobayashi. A program for branching problems in the representation
theory of real reductive groups. Progr. Math.312, pp. 277-322, 2015.
- T. Kobayashi, T. Kubo, and M. Pevzner, Conformal symmetry breaking
operators for differential forms on spheres, Lecture Notes in Math.,
2170, Springer, 2016. viii+192 pages.
- T. Kobayashi, B. Speh. Symmetry Breaking for Representations of Rank
One Orthogonal Groups, Memoirs of AMS. 238. 2015. vi+118 pages.
- T. Kobayashi, B. Speh, Symmetry Breaking for Representations of
Rank One Orthogonal Groups II, Lecture Notes in Math. 2234,
Springer, 2018. xv+342 pages.

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© Toshiyuki Kobayashi