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In this paper we show that the systems introduced in [12] and [22] are equivalent, both giving the notion of quaternionic Hermitian monogenic functions. This makes it possible to prove that the free resolution associated to the system is linear in any dimension, and that the first cohomology module is nontrivial, thus generalizing the results in [22]. Furthermore, exploiting the decomposition of the spinor space into sp(m)-irreducibles, we find a certain number of "algebraic" compatibility conditions for the system, suggesting that the usual spinor reduction is not applicable.


This article was originally published in Advances in Geometry, volume 11, issue 1, in 2011. DOI: 10.1515/ADVGEOM.2010.045

Peer Reviewed



Walter de Gruyter GMBH



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