Spinor-valued and Clifford algebra-valued harmonic polynomials

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We give decompositions of the spinor-valued and the Clifford algebra-valued harmonic polynomials on Rn. In order to do so, we consider some differential complexes and show that these are exact. As a corollary, we have Poincaré lemma for harmonic polynomials. Besides, we prove that each component of the decompositions is an irreducible representation space with respect to Spin(n).

Original languageEnglish
Pages (from-to)201-215
Number of pages15
JournalJournal of Geometry and Physics
Volume37
Issue number3
DOIs
Publication statusPublished - 2001 Feb 1

Keywords

  • 43A85
  • 43A90
  • 58J05
  • Clifford-valued polynomials
  • Invariant operators
  • Spin(n) -modules
  • Spinors
  • Twistors

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

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