Theory of prehomogeneous vector spaces. II: A supplement (Q1364338)

The paper is a supplement to a previous paper [see \textit{A. Gyoja}, Publ. Res. Inst. Math. Sci. 27, No. 6, 861-922 (1991; Zbl 0773.14025)]. Like the former paper it deals with prehomogeneous vector spaces with respect to a connected reductive group. The results of that paper about the Fourier transform of a complex power \(f^\alpha\) of a relative invariant polynomial function \(f\) are extended to more general \(D\)-modules of the form \(D(f^\alpha u)\) where \(u\) is a section of a regular holonomic \(D\)-module and \(Du\) is an integrable connection of rank one with some additional properties.