b-Functions of Prehomogeneous Vector Spaces of Dynkin–Kostant Type for Exceptional Groups

The purpose of this paper is to determine the b-functions of all the prehomogeneous vector spaces associated to nilpotent orbits in the Dynkin–Kostant theory for all the complex simple algebraic groups of exceptional type. Our method to calculate b-functions is based on the structure theorem for b-functions of several variables and the functional equations for them.