Invariant resolutions for several Fueter operators |
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| Institution: | 1. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy;2. Mathematical Institute, Charles University, Sokolovská 83, Praha, Czech Republic;3. Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA;1. Institute of Mathematics, USC, RAS, Russia;2. Institute of Mathematics, University of Potsdam, Germany;1. Middle East Technical University, Department of Mathematics, 06531 Ankara, Turkey;2. Gazi Üniversitesi, Fen Fakültesi, Matematik Bölümü, 06500 Teknikokullar, Ankara, Turkey |
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| 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). |
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