Conformal covariance for the powers of the Dirac operator

Abstract

A new proof of the conformal covariance of the powers of the flat Dirac operator is obtained. The proof uses their relation with the Knapp-Stein intertwining operators for the spinorial principal series. We also treat the compact picture, i.e. the corresponding operators on the sphere, where certain polynomials of the Dirac operator appear. This gives a new representation-theoretic framework for earlier results.

References in corpus (2)

• On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
• Spontaneous generation of eigenvalues

Cited by in corpus (6)

• Knapp-Stein Type Intertwining Operators for Symmetric Pairs II. -- The Translation Principle and Intertwining Operators for Spinors
• On Some Conformally Invariant Operators in Euclidean Space
• Construction of Arbitrary Order Conformally Invariant Operators in Higher Spin Spaces
• Some Properties of the Higher Spin Laplace Operator
• Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations
• Polynomial Null Solutions to Bosonic Laplacians, Bosonic Bergman and Hardy Spaces