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arXiv · 1712.09212

Conformal symmetry breaking on differential forms and some applications

Toshiyuki Kobayashi
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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 [Memoirs of Amer.Math.Soc. 2015]) and the case of local operators (Kobayashi--Kubo--Pevzner [Lecture Notes in Math. 2016]). Some applications to automorphic form theory, motivations from conformal geometry, and the methods of proof are also discussed.

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Toshiyuki Kobayashi. 2017-12-26. Conformal symmetry breaking on differential forms and some applications. https://doi.org/10.1007/978-3-030-01156-7_32

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