Penrose transform and monogenic functions

TL;DR

This paper explicitly constructs the isomorphism provided by the Penrose transform between the kernel of an invariant differential operator and sheaf cohomology on twistor space, facilitating future research.

Contribution

It provides an explicit formulation of the Penrose transform isomorphism, which was previously understood abstractly, enabling detailed analysis of the complex's properties.

Findings

Explicit form of the Penrose transform isomorphism derived

Facilitates further investigation into the properties of the associated complex

Enhances understanding of the relationship between differential operators and sheaf cohomology

Abstract

Penrose transform tells us that there is an isomorphism of the kernel of an invariant differential operator studied in the paper [TS] and sheaf cohomology of some vector bundle on twistor space. The point of this paper is to write down this isomorphism explicitly. Explicit form of the isomorphism will be crucial for further investigation on the properties of the complex.