scholarly journals A classification of 3-simple prehomogeneous vector spaces of nontrivial type

1996 ◽  
Vol 22 (1) ◽  
pp. 159-198 ◽  
Author(s):  
Tatsuo KIMURA ◽  
Kosei UEDA ◽  
Takeshi YOSHIGAKI
Keyword(s):  
Vector Spaces ◽  
Prehomogeneous Vector Spaces

scholarly journals A classification of 2-simple prehomogeneous vector spaces of type I

1988 ◽  
Vol 114 (2) ◽  
pp. 369-400 ◽  
Author(s):  
Tatsuo Kimura ◽  
Shin-ichi Kasai ◽  
Masaaki Inuzuka ◽  
Osami Yasukura
Keyword(s):  
Vector Spaces ◽  
Type I ◽  
Prehomogeneous Vector Spaces

Some P.V.-Equivalences and a Classification of 2-Simple Prehomogeneous Vector Spaces of Type II

1988 ◽  
Vol 308 (2) ◽  
pp. 433 ◽  
Author(s):  
Tatsuo Kimura ◽  
Shin-Ichi Kasai ◽  
Masanobu Taguchi ◽  
Masaaki Inuzuka
Keyword(s):  
Vector Spaces ◽  
Type Ii ◽  
Prehomogeneous Vector Spaces

scholarly journals A classification of irreducible prehomogeneous vector spaces and their relative invariants

1977 ◽  
Vol 65 ◽  
pp. 1-155 ◽  
Author(s):  
M. Sato ◽  
T. Kimura
Keyword(s):  
Vector Space ◽  
Linear Algebraic Group ◽  
Vector Spaces ◽  
Rational Representation ◽  
Finite Dimensional Vector Space ◽  
Prehomogeneous Vector Space ◽  
Finite Dimensional ◽  
Prehomogeneous Vector Spaces ◽  
Relative Invariants

LetGbe a connected linear algebraic group, andpa rational representation ofGon a finite-dimensional vector spaceV, all defined over the complex number fieldC.We call such a triplet (G, p, V) aprehomogeneous vector spaceifVhas a Zariski-denseG-orbit. The main purpose of this paper is to classify all prehomogeneous vector spaces whenpis irreducible, and to investigate their relative invariants and the regularity.

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