Equivariant differential operators on spinors in conformal geometry

Abstract

We present a novel approach to the classification of conformally equivariant differential operators on spinors in the case of homogeneous conformal geometry. It is based on the classification of solutions for a vector-valued system of partial differential equations, associated to D-modules for the homogeneous conformal structure and controlled by the spin Howe duality for the orthogonal Lie algebras.

Keywords

• Conformal structure
• D-modules
• spinor representation
• generalized Verma modules
• conformally equivariant differential operators