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

    Fingerprint

    Harmonic Polynomials
    Clifford Algebra
    Spinor
    polynomials
    algebra
    harmonics
    decomposition
    Decompose
    Irreducible Representation
    Lemma
    Corollary
    theorems

    Keywords

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

    ASJC Scopus subject areas

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

    Cite this

    Spinor-valued and Clifford algebra-valued harmonic polynomials. / Homma, Yasushi.

    In: Journal of Geometry and Physics, Vol. 37, No. 3, 02.2001, p. 201-215.

    Research output: Contribution to journalArticle

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