I begin with 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. 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, 314 pages, arXiv: 1801.00158.

© Toshiyuki Kobayashi