Abstract.
The Dirac operator in several operators is an analogue of the \(\bar {\partial}\)- operator in theory of several complex variables. The Hartog’s type phenomena are encoded in a complex of invariant differential operators starting with the Dirac operator, which is an analogue of the Dolbeault complex. In the paper, a construction of the complex is given for the Dirac operator in 4 variables in dimension 6 (i.e. in the non-stable range). A peculiar feature of the complex is that it contains a third order operator. The methods used in the construction are based on the Penrose transform developed by R. Baston and M. Eastwood.
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To Jarolím Bureš, my teacher and friend.
Received: October, 2007. Accepted: February, 2008.
The work presented here is a part of the research project MSM 0021620839 and was supported also by the grant GA ČR 201/05/2117.
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Krump, L. A Resolution for the Dirac Operator in Four Variables in Dimension 6. AACA 19, 365–374 (2009). https://doi.org/10.1007/s00006-009-0169-0
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DOI: https://doi.org/10.1007/s00006-009-0169-0