# Penrose transform and monogenic sections

## Tomáš Salač

Address: Faculty of Mathematics and Physics, Mathematical Institute, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic

E-mail: salac@karlin.mff.cuni.cz

Abstract: The Penrose transform gives an isomorphism between the kernel of the $2$-Dirac operator over an affine subset and the third sheaf cohomology group on the twistor space. In the paper we give an integral formula which realizes the isomorphism and decompose the kernel as a module of the Levi factor of the parabolic subgroup. This gives a new insight into the structure of the kernel of the operator.

AMSclassification: primary 35A22; secondary 58J10.

Keywords: Penrose transform, monogenic spinors.

DOI: 10.5817/AM2012-5-399