Lefschetz Principle in the Theory of Prehomogeneous Vector Spaces

2018 ◽  
Author(s):  
Akihiko Gyoja
Keyword(s):  
Vector Spaces ◽  
Prehomogeneous Vector Spaces ◽  
Lefschetz Principle

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 On the convergence of the zeta function for certain prehomogeneous vector spaces

1995 ◽  
Vol 140 ◽  
pp. 1-31 ◽  
Author(s):  
Akihiko Yukie
Keyword(s):  
Invariant Measure ◽  
Zeta Function ◽  
Complex Variable ◽  
Vector Spaces ◽  
Invariant Polynomial ◽  
Connected Component ◽  
Relative Invariant ◽  
Prehomogeneous Vector Space ◽  
Prehomogeneous Vector Spaces ◽  
Rational Character

Let (G, V) be an irreducible prehomogeneous vector space defined over a number field k, P ∈ k[V] a relative invariant polynomial, and χ a rational character of G such that . For , let Gx be the stabilizer of x, and the connected component of 1 of Gx. We define L0 to be the set of such that does not have a non-trivial rational character. Then we define the zeta function for (G, Y) by the following integralwhere Φ is a Schwartz-Bruhat function, s is a complex variable, and dg” is an invariant measure.

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