On Conformal Powers of the Dirac Operator on Einstein Manifolds

Abstract

We determine the structure of conformal powers of the Dirac operator on Einstein {\it Spin}-manifolds in terms of the product formula for shifted Dirac operators. The result is based on the techniques of higher variations for the Dirac operator on Einstein manifolds and spectral analysis of the Dirac operator on the associated Poincaré-Einstein metric, and relies on combinatorial recurrence identities related to the dual Hahn polynomials.

Conformal and semi-Riemannian {\it Spin}-geometry, conformal powers of the Dirac operator, Einstein manifolds, higher variations of the Dirac operator, Hahn polynomials