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) = (Sⁿ, Sⁿ⁻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 proofs are also discussed.