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Polynomial invariants for the rarita-schwinger operator

  • David Eelbode
  • Dalibor Šmíd
Part of the Trends in Mathematics book series (TM)

Abstract

We show that polynomial invariant operators on functions with values in the Spin(n)-representation with highest weight (3/2,1/2,…,1/2) are spanned by powers of the symbols of the Laplace and Rarita-Schwinger operators. This result generalizes the well-known description of polynomial invariants on the scalar and spinor-valued functions. We describe the operators in the language of Clifford analysis.

Keywords

Rarita-Schwinger operator Fischer decomposition Invariant polynomials 

Mathematics Subject Classification (2000)

15A66 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • David Eelbode
    • 1
  • Dalibor Šmíd
    • 2
  1. 1.Clifford Research Group Dept. of Mathematical AnalysisGhent University Galglaan 2GhentBelgium
  2. 2.Mathematical InstituteCharles UniversityPrague 8Czech Republic

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