Filtered Stokes G-local Systems in Nonabelian Hodge Theory on Curves

In the wild nonabelian Hodge correspondence on curves, filtered Stokes G-local systems are regarded as the objects on the Betti side. In this paper, we demonstrate a construction of the moduli space of them, called the Betti moduli space, it will reduce to the wild character variety when the Betti weights are trivial. We study some particular examples including Eguchi-Hanson space and the Airy equation together with the corresponding moduli spaces. Furthermore, we provide a proof of the correspondence among irregular singular G-connections, Stokes G-local systems, and Stokes G-representations to fill a gap in the literature. This correspondence can be viewed as the G-version of irregular Rieman-Hilbert correspondence on curves.