Jordan Decomposition for Formal G-Connections

A theorem of Hukuhara, Levelt, and Turrittin states that every formal differential operator has a Jordan decomposition. This theorem was generalised by Babbit and Varadarajan to the case of formal $G$-connections where $G$ is a semisimple group. In this paper, we provide straightforward proofs of these facts, highlighting the analogy between the linear and differential settings.