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A classification of irreducible prehomogeneous vector spaces and their relative invariants

Published online by Cambridge University Press:  22 January 2016

M. Sato  and
T. Kimura
M. Sato
Affiliation:
The Research Institute for Mathematical Science, Kyoto University, Nagoya University and The Institute for Advanced Study, Princeton
T. Kimura
Affiliation:
The Research Institute for Mathematical Science, Kyoto University, Nagoya University and The Institute for Advanced Study, Princeton
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Let G be a connected linear algebraic group, and p a rational representation of G on a finite-dimensional vector space V, all defined over the complex number field C.

We call such a triplet (G, p, V) a prehomogeneous vector space if V has a Zariski-dense G-orbit. The main purpose of this paper is to classify all prehomogeneous vector spaces when p is irreducible, and to investigate their relative invariants and the regularity.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 65 , March 1977 , pp. 1 - 155
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

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