### Abstract

We give decompositions of the spinor-valued and the Clifford algebra-valued harmonic polynomials on R^{n}. 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 | |

Publication status | Published - 2001 Feb |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Journal of Geometry and Physics*, vol. 37, no. 3, pp. 201-215. https://doi.org/10.1016/S0393-0440(00)00045-0

}

TY - JOUR

T1 - Spinor-valued and Clifford algebra-valued harmonic polynomials

AU - Homma, Yasushi

PY - 2001/2

Y1 - 2001/2

N2 - 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).

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

UR - http://www.scopus.com/inward/record.url?scp=0041405533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041405533&partnerID=8YFLogxK

U2 - 10.1016/S0393-0440(00)00045-0

DO - 10.1016/S0393-0440(00)00045-0

M3 - Article

VL - 37

SP - 201

EP - 215

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

IS - 3

ER -