The source operator method: an overview

TL;DR

This paper reviews the source operator method for constructing symmetry breaking differential operators in conformal geometry, highlighting its applications to tensor products, differential forms, spinors, and sphere restrictions.

Contribution

It provides an overview of the source operator method and demonstrates its versatility across various geometric and representation-theoretic contexts.

Findings

Unified framework for constructing SBDOs in conformal groups

Applications to differential forms and spinors

Extension to sphere restriction operators

Abstract

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 $S^{n-1}$.