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

Jan Frahm ; Bent Ørsted

Symmetry, integrability and geometry: methods and applications, Tome 15 (2019)

Résumé

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.

Détail

Keywords: Knapp–Stein intertwiners, intertwining operators, symmetry breaking operators, symmetric pairs, translation principle.
Mots-clés : principal series

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