Title | **Invariant resolutions for several Fueter operators** |

Author(s) | Fabrizio Colombo, Vladimir Souček, Daniele C. Struppa |

Type | Article in Journal |

Abstract | A proper generalization of complex function theory to higher dimension is Clifford analysis and an analogue of holomorphic functions of several complex variables were recently described as the space of solutions of several Dirac equations. The four-dimensional case has special features and is closely connected to functions of quaternionic variables. In this paper we present an approach to the Dolbeault sequence for several quaternionic variables based on symmetries and representation theory. In particular we prove that the resolution of the Cauchy–Fueter system obtained algebraically, via Gröbner bases techniques, is equivalent to the one obtained by R.J. Baston (J. Geom. Phys. 1992). |

Keywords | Cauchy–Fueter complex, Overdetermined differential operators, Symmetry and representation theory, Parabolic geometries |

ISSN | 0393-0440 |

URL |
http://www.sciencedirect.com/science/article/pii/S0393044005001002 |

Language | English |

Journal | Journal of Geometry and Physics |

Volume | 56 |

Number | 7 |

Pages | 1175 - 1191 |

Year | 2006 |

Edition | 0 |

Translation |
No |

Refereed |
No |