Conformal Symmetry Breaking on Differential Forms and Some Applications

Abstract

Rapid progress has been made recently on symmetry breaking operators for real reductive groups. Based on Program A-C for branching problems (T. Kobayashi [Progr. Math. 2015]), we illustrate a scheme of the classification of (local and nonlocal) symmetry breaking operators by an example of conformal representations on differential forms on the model space (X, Y ) = (S n , S n−1 ), which generalizes the scalar case (Kobayashi-Speh [Mem. Amer. Math. Soc. 2015]) and the case of local operators (Kobayashi-Kubo-Pevzner [Lect. Notes Math. 2016]). Some applications to automorphic form theory, motivations from conformal geometry, and the methods of proof are also discussed.