scholarly journals Structure and orbits of certain prehomogeneous vector spaces related with orthogonal roots

1996 ◽  
Vol 72 (5) ◽  
pp. 104-107 ◽  
Author(s):  
Iris Muller
Keyword(s):  
Vector Spaces ◽  
Prehomogeneous Vector Spaces

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.

On Zeta Functions Associated with Prehomogeneous Vector Spaces

1974 ◽  
Vol 100 (1) ◽  
pp. 131 ◽  
Author(s):  
Mikio Sato ◽  
Takuro Shintani
Keyword(s):  
Zeta Functions ◽  
Vector Spaces ◽  
Prehomogeneous Vector Spaces
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