Igusa Local Zeta Functions and Parabolic Castling Transformation of Prehomogeneous Vector Spaces Original Research Article

The castling transformation is a standard procedure of constructing new prehomogeneous vector spaces from a given one. Professor J.-I. Igusa gives a relation between the Igusa local zeta function of a prehomogeneous vector space and the Igusa local zeta function of its castling transform. Y. Teranishi gives one generalization of the castling transformation. This generalized castling transformation is related to parabolic subgroups, hence we call it the parabolic castling transformation. In this paper, we give a relation between the Igusa local zeta function of a prehomogeneous vector space and the Igusa local zeta function of its parabolic castling transform.