Mathematische Zeitschrift

, Volume 280, Issue 3–4, pp 825–839 | Cite as

On conformal powers of the Dirac operator on Einstein manifolds

  • Matthias Fischmann
  • Christian Krattenthaler
  • Petr Somberg
Article

Abstract

We determine the structure of conformal powers of the Dirac operator on Einstein 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.

Keywords

Conformal and semi-Riemannian Spin-geometry Conformal powers of the Dirac operator Einstein manifolds Higher variations of the Dirac operator  Hahn polynomials 

Mathematics Subject Classification

53C27 34L40 53A30 33C20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Matthias Fischmann
    • 1
  • Christian Krattenthaler
    • 2
  • Petr Somberg
    • 1
  1. 1.E. Čech InstituteMathematical Institute of Charles UniversityPrague 8Czech Republic
  2. 2.Fakultät für MathematikUniversität WienViennaAustria

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