Quaternionic complexes
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.
scientific article; zbMATH DE number 34537
scientific article