## 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*)=(*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 proofs are also discussed.

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© Toshiyuki Kobayashi