# Knapp-Stein Type Intertwining Operators for Symmetric Pairs II. -- The Translation Principle and Intertwining Operators for Spinors

## TL;DR

This paper extends the construction of symmetry breaking operators for reductive group pairs, explicitly describing their integral kernels and classifying operators between spinor representations in a conformal setting.

## Contribution

It introduces a broad class of meromorphic symmetry breaking operators for generalized principal series and classifies spinor intertwining operators for conformal groups.

## Key findings

- Explicit integral kernel formulas for symmetry breaking operators.
- Complete classification of spinor intertwining operators.
- Extension of previous constructions to a larger class of representations.

## Abstract

For a symmetric pair $(G,H)$ of reductive groups we extend to a large class of generalized principal series representations our previous construction of meromorphic families of symmetry breaking operators. These operators intertwine between a possibly vector-valued principal series of $G$ and one for $H$ and are given explicitly in terms of their integral kernels. As an application we give a complete classification of symmetry breaking operators from spinors on a Euclidean space to spinors on a hyperplane, intertwining for a double cover of the conformal group of the hyperplane.