We discuss restrictions of irreducible representations to reductive subgroups with focus on geometric question:[ abstract (pdf) ]If time permits, we shall also discuss the following related questions for orthogonal groups of rank one.

- Classification of confomally covariant symmetry breaking operators on differential forms.

- Period of irreducible unitary representations.
- Occurrence of complementary series representations in branching laws.
Refereces

- 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.

© Toshiyuki Kobayashi