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A duality for homogeneous bundles on twistor space. (English) Zbl 0534.14008

A particular aspect of Penrose’s twistor theory is the description of classical massless fields as cohomology classes on open subsets of complex projective 3-space with coefficients in powers of the Hopf bundle. Each field can be represented in two ways and this gives rise to a duality in the form of an isomorphism known as the twistor transform [M. G. Eastwood and M. L. Ginsberg, Duke Math. J. 48, 177-196 (1981; Zbl 0483.55004)]. - This article studies what happens if the coefficient bundle is replaced by an arbitrary homogeneous bundle. The duality generalizes for a natural class of bundles.
The exposition is in purely mathematical terms i. e. avoiding the physical considerations which provide motivation.

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
53C80 Applications of global differential geometry to the sciences
32C37 Duality theorems for analytic spaces
43A85 Harmonic analysis on homogeneous spaces

Citations:

Zbl 0483.55004
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