Conformal Symmetry Breaking on Differential Forms and Some Applications
Conformal Symmetry Breaking on Differential Forms and Some Applications
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DOI：
10.1007/978-3-030-01156-7_32
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发表时间：
2017-12
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影响因子：
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通讯作者：
Toshiyuki Kobayashi
中科院分区：
文献类型：
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作者：
Toshiyuki Kobayashi
真实的约化群对称破缺算子的研究近年来取得了很大进展。本文基于分支问题的A-C程序（T.小林Math.2015]），我们说明了一种分类方案，（局部和非局部）对称破缺算子，以模型空间（X，Y）=（Sn，Sn-1）上微分形式的保角表示为例，它概括了标量的情况（Kobayashi-Speh [Mem. Amer. Math. Soc. 2015]）和局部算子的情况（Kobayashi-Kubo-Pevzner [Lect. Notes Math. 2016]）。自守形式理论的一些应用，共形几何的动机，以及证明的方法也进行了讨论。
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.