Spinor-valued and Clifford algebra-valued harmonic polynomials

Yasushi Homma

doi:10.1016/S0393-0440(00)00045-0

Spinor-valued and Clifford algebra-valued harmonic polynomials

Yasushi Homma^*

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	201-215
Number of pages	15
Journal	Journal of Geometry and Physics
Volume	37
Issue number	3
DOIs	https://doi.org/10.1016/S0393-0440(00)00045-0
Publication status	Published - 2001 Feb

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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10.1016/S0393-0440(00)00045-0

Cite this

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AB - 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).

KW - 43A85

KW - 43A90

KW - 58J05

KW - Clifford-valued polynomials

KW - Invariant operators

KW - Spin(n) -modules

KW - Spinors

KW - Twistors

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EP - 215

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

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ER -

Spinor-valued and Clifford algebra-valued harmonic polynomials

Abstract

Keywords

ASJC Scopus subject areas

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