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

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.