Complex Analysis and Operator Theory

, Volume 6, Issue 5, pp 1011–1023 | Cite as

Factorization of Laplace Operators on Higher Spin Representations

  • David Eelbode
  • Dalibor ŠmídEmail author


This paper deals with the problem of factorizing integer powers of the Laplace operator acting on functions taking values in higher spin representations. This is a far-reaching generalization of the well-known fact that the square of the Dirac operator is equal to the Laplace operator. Using algebraic properties of projections of Stein–Weiss gradients, i.e. generalized Rarita–Schwinger and twistor operators, we give a sharp upper bound on the order of polyharmonicity for functions with values in a given representation with half-integral highest weight.


Clifford algebras Laplace operator Dirac and Rarita–Schwinger operators 

Mathematics Subject Classification (2000)

Primary 30G35 Secondary 20G05 31A30 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of AntwerpAntwerpBelgium
  2. 2.Mathematical InstituteCharles University PraguePraha 8Czech Republic

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