On Conformal Powers of the Dirac Operator on Einstein Manifolds

TL;DR

This paper characterizes conformal powers of the Dirac operator on Einstein spin-manifolds using product formulas, spectral analysis, and combinatorial identities, advancing understanding of geometric analysis in this context.

Contribution

It provides a new explicit structure for conformal powers of the Dirac operator on Einstein manifolds, combining spectral and combinatorial techniques.

Findings

Explicit product formula for conformal powers of the Dirac operator

Spectral analysis connecting Dirac operators on Einstein and Poincaré-Einstein manifolds

Use of dual Hahn polynomial identities in geometric analysis

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 Poincar\'e-Einstein metric, and relies on combinatorial recurrence identities related to the dual Hahn polynomials.