The Classification of Rigid Irregular G_2-Connections

We outline how to construct families of rigid irregular G_2-connections which are non-hypergeometric. This construction is carried out using the Katz-Arinkin algorithm for irregular connections which involves middle convolution and Fourier transform of connections. Using methods of differential Galois theory we obtain a complete
classification of irreducible rigid irregular G_2-connections generalizing the result of Dettweiler Reiter on the classification of rigid G_2-local systems in the setting with complex base field.