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Zeta functions of prehomogeneous affine spaces

Published online by Cambridge University Press:  22 January 2016

Atsushi Murase  and
Takashi Sugano
Atsushi Murase
Affiliation:
Faculty of Science, Kyoto Sangyo University, MotoyamaKamigamo, 603 Kyoto, Japan
Takashi Sugano
Affiliation:
Faculty of Science, Hiroshima University, 1-3-1 Kagamiyama, 724 Higashi-Hiroshima, Japan
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Let ρ be an algebraic homomorphism of a linear algebraic group G into the affine transformation group Aff(V) of a finite dimensional vector space V. We say that a triplet (G, V, ρ) is a prehomogeneous affine space, if there exists a proper algebraic subset S of V such that V — S is a single ρ(G)-orbit. In particular, (G, V, ρ) is a usual prehomogeneous vector space (PV, briefly) in the case where ρ(G) ⊂ GL(V) (cf. [5], [7]). In the preceding paper [2], we defined zeta functions associated with certain prehomogeneous affine spaces and proved their analytic continuation and functional equations.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 132 , December 1993 , pp. 91 - 114
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

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