On M. Sato's Classification of Some Reductive Prehomogeneous Vector Spaces

Tatsuo Kimura; Yukimi Ishii; Inhyun Ryu; Michio Hamada; Yoshiteru Kurosawa; Masaya Ouchi; Tomohiro Kamiyoshi

doi:10.2977/prims/40

JournalsprimsVol. 47, No. 2pp. 397–418

On M. Sato's Classification of Some Reductive Prehomogeneous Vector Spaces

Tatsuo Kimura
University of Tsukuba, Ibaraki, Japan
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Yukimi Ishii
University of Tsukuba, Ibaraki, Japan
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Inhyun Ryu
University of Tsukuba, Ibaraki, Japan
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Michio Hamada
University of Tsukuba, Ibaraki, Japan
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Yoshiteru Kurosawa
University of Tsukuba, Ibaraki, Japan
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Masaya Ouchi
University of Tsukuba, Ibaraki, Japan
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Tomohiro Kamiyoshi
University of Tsukuba, Ibaraki, Japan
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Abstract

Under some condition, M. Sato classified reductive prehomogeneous vector spaces of the form $(G_{0} \times G, Λ_{1} \otimes ρ, V (n) \otimes V)$ . 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 $C$ .

Cite this article

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. 397–418

DOI 10.2977/PRIMS/40