Under some condition, M. Sato classified reductive prehomogeneous vector spaces of the form . In this paper, under the other condition, we classify the prehomogeneous vector spaces of the same form. We consider everything over the complex number field .
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Tatsuo Kimura, Yukimi Ishii, Inhyun Ryu, Michio Hamada, Yoshiteru Kurosawa, Masaya Ouchi, Tomohiro Kamiyoshi, On M. Sato's Classification of Some Reductive Prehomogeneous Vector Spaces. Publ. Res. Inst. Math. Sci. 47 (2011), no. 2, pp. 397–418DOI 10.2977/PRIMS/40