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This is an overview on the source operator method, which leads to the construction of symmetry breaking differential operators (SBDO) in the context of tensor product of two principals series representations for the conformal group of a simple real Jordan algebra. This method can be applied to other geometric contexts: in the construction of SBDO for differential forms and for spinors and also for the construction of Juhl’s operators corresponding to the restriction from the sphere \(S^n\) to \(S^{n-1}\) .

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The Source Operator Method: An Overview

  • 章节

  • 发表日期：

    2025年

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  • Salem Ben Said,
  • Jean-Louis Clerc,
  • Khalid Koufany

摘要

This is an overview on the source operator method, which leads to the construction of symmetry breaking differential operators (SBDO) in the context of tensor product of two principals series representations for the conformal group of a simple real Jordan algebra. This method can be applied to other geometric contexts: in the construction of SBDO for differential forms and for spinors and also for the construction of Juhl’s operators corresponding to the restriction from the sphere \(S^n\) to \(S^{n-1}\) .