  We establish normal form theorems for a large class of singular flat
connections on complex manifolds, including connections with logarithmic poles
along weighted homogeneous Saito free divisors. As a result, we show that the
moduli spaces of such connections admit the structure of algebraic quotient
stacks. In order to prove these results, we introduce homogeneous Lie groupoids
and study their representation theory. In this direction, we prove two main
results: a Jordan-Chevalley decomposition theorem, and a linearization theorem.
We give explicit normal forms for several examples of free divisors, such as
homogeneous plane curves, reductive free divisors, and one of Sekiguchi's free
divisors.
