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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

[1] Brylinski, J-L. and Delorme, P., Vecteurs distributions H-invariants pour les séries principales généralisées d’espaces symétriques reductifs et prolongement meromorphe d’intégrales d’Eisenstein, Invent. Math., 109 (1992), 619–664.Google Scholar
[2] Murase, A. and Sugano, T., A note on zeta functions associated with certain prehomogeneous affine spaces, Advanced Studies in Pure Math., 15 (1989), 415–428.Google Scholar
[3] Sato, F., Zeta functions in several variables associated with prehomogeneous vector spaces I: Functional equations, Tohoku Math. J., 34 (1982), 437–483.Google Scholar
[4] Sato, F., On functional equations of zeta distributions, Advanced Studies in Pure Math., 15 (1989), 465–508.Google Scholar
[5] Sato, M., Theory of prehomogeneous vector spaces (notes by T. Shintani in Japanese), Sugaku no Ayumi, 15 (1970), 85–157.Google Scholar
[6] Sato, M., Kashiwara, M., Kimura, T., Oshima, T., Micro local analysis of prehomogeneous vector spaces, Invent. Math., 62 (1980), 117–179.CrossRefGoogle Scholar
[7] Sato, M., Kimura, T., A classification of irreducible prehomogeneous vector spaces and their invariants, Nagoya Math. J., 65 (1977), 1–155.Google Scholar
[8] Sato, M., Shintani, T., On zeta functions associated with prehomogeneous vector spaces, Ann. of Math., 100 (1974), 131–170.Google Scholar