Relative invariants of 2-simple prehomogeneous vector spaces of type I

In the present paper, by using equivariant maps, we construct explicitly relative invariants of the 2-simple prehomogeneous vector spaces of type I, which are classified in [T. Kimura, S. Kasai, M. Inuzuka, O. Yasukura, A classification of 2-simple prehomogeneous vector spaces of type I, J. Algebra 114 (1988) 369–400]. This is a continuation of our previous work [T. Kogiso, G. Miyabe, M. Kobayashi, T. Kimura, Non-regular 2-simple prehomogeneous vector spaces of type I and their relative invariants, J. Algebra 251 (2002) 27–69; T. Kogiso, G. Miyabe, M. Kobayashi, T. Kimura, Relative invariants of some 2-simple prehomogeneous vector spaces, Math. Comp. 72 (2003) 865–889].