Coupling solutions of BGG-equations in conformal spin geometry (Q2428145)

A simple formula for necessary and sufficient additional integrability conditions for a solution of BGG-equations (that is, geometric overdetermined systems of PDEs on parabolic geometries) to be normal, is given. Then, the author discusses a procedure for coupling known solutions of BGG-equations to produce new ones. Using a suitable calculus for conformal spin structures, this yields explicit coupling formulas and conditions between almost Einstein scales, conformal Killing fields and twistor spinors. A class of generic twistor spinors that provides an invariant decomposition of conformal Killing fields is also analyzed.