Middle convolution and Harnad duality

Dettweiler-Reiter's additive description of Katz's middle convolution can be interpreted in terms of the Harnad duality. Using this interpretation together with Mumford's geometric invariant theory, we generalize the additive middle convolution to have a multi-parameter and act on systems of linear ordinary differential equations with irregular singularities. We show that the generalized operation holds basic properties of the original one, and additionally, show that Katz's algorithm involving our generalization works well in generic case.