\(b\)-functions of regular simple prehomogeneous vector spaces (Q1861082)

The article deals with the explicit description of the \(b\)-functions of regular simple prehomogeneous vector spaces. In fact, most of these \(b\)-functions have been described by several authors and mainly by \textit{S. Kasai} [On the \(b\)-functions of regular prehomogeneous vector spaces of simple algebraic groups (in Japanese), RIMS Kokyuroku 929, 31-81 (1987)]. In the present paper the author describes the corresponding \(b\)-function for the two remaining regular simple prehomogeneous vector spaces. As the cited article of S. Kasai is in Japanese, an appendix contains a complete table of \(b\)-functions for all regular simple prehomogeneous vector spaces.