T. Kobayashi. Conformal symmetry breaking on differential forms and some applications. In P. Kielanowski, A. Odzijewicz, and E. Previato, editors, Geometric Methods in Physics XXXVI workshop 2017, Trends in Mathematics, pages 289-308. Birkhäuser, Cham, 2019. DOI: 10.1007/978-3-030-01156-7_32. arXiv: 1712.09212..

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.

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