Quaternionic complexes. (English) Zbl 0764.53022

The author studies a quaternion analogue of Dolbeault cohomology obtained by extending the Moisil-Fueter operator from quaternion analysis to a locally exact complex. He uses some Bernstein-Gelfand-Gelfand complexes in representation theory, the Penrose transform and the twistor theory of quaternionic manifolds. The obtained complexes correspond to the semiregular orbits of the Weyl group of \(\text{sl}(2n+2,\mathbb{C})\). In the hyper-Kähler case the author computes the index of these complexes showing that the obtained quaternion cohomology is not trivial.
Reviewer: V.Oproiu (Iaşi)


53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
55N30 Sheaf cohomology in algebraic topology
32C35 Analytic sheaves and cohomology groups
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