Igusa local zeta functions and parabolic castling transformation of prehomogeneous vector spaces (Q1284205)

The castling transformation is a standard procedure for constructing new prehomogeneous vector spaces from a given one and plays a crucial role in the classification of prehomogeneous vector spaces. \textit{J. I. Igusa} [Am. J. Math. 110, 197-233 (1988; Zbl 0662.12014)] gives a relation between the Igusa local zeta function of a prehomogeneous vector space and the Igusa local zeta function of its castling transformation. \textit{Y. Teranishi} [Nagoya Math. 98, 139-156 (1985; Zbl 0573.20041)] gave a generalization of the castling transformation related to parabolic subgroups. In this paper, a relation between the Igusa local zeta function of a prehomogeneous vector space and the Igusa local zeta functions of its parabolic castling transformation is obtained.