Equivariant differential operators on spinors in conformal geometry

TL;DR

This paper introduces a new method for classifying conformally equivariant differential operators on spinors using solutions of PDE systems linked to $\

Contribution

It develops a classification approach based on $\

Findings

Classification of solutions for PDE systems related to conformal structures

Application of spin Howe duality to classify differential operators

Framework applicable to homogeneous 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 $\mathcal{D}$-modules for the homogeneous conformal structure and controlled by the spin Howe duality for the orthogonal Lie algebras.