Symmetry Breaking Operators in Conformal Geometry (opening lecture). Joint meeting of X. International Symposium QUANTUM THEORY AND SYMMETRIES and XII. International Workshop ''Lie Theory and Its Applications in Physics”. Varna, Bulgaria, 19-25 June 2017.

I plan to discuss a general program to understand the restriction of infinite-dimensional representations of reductive groupsy in three stages, and then illustrate it by an example arising from conformal geometry. In particular, I present a complete classification of conformally covariant symmetry breaking operators on differential forms for a certain model case. If time permits, I also give a flavor of some applications to automorphic forms.

T. Kobayashi. A program for branching problems in the representation theory of real reductive groups. Progr. Math. vol. 312, pp. 277-322, 2015, Birkhauser.
T. Kobayashi, T. Kubo, and M. Pevzner, Conformal symmetry breaking operators for differential forms on spheres, Lecture Notes in Math. vol. 2170, 2016, Springer.
T. Kobayashi and B. Speh, Symmetry Breaking for Representations of Rank One Orthogonal Groups, Memoirs of Amer. Math. Soc. vol. 238. 2015, AMS.

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