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The functional equation of zeta distributions associated with prehomogeneous vector spaces

Published online by Cambridge University Press:  22 January 2016

Yasuo Teranishi*
Affiliation:
Department of Mathematics, Faculty of Science, Nagoya University, Chikusan-ku, Nagoya 464, Japan
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Let (G, ρ, V) be a triple of a linear algebraic group G and a rational representation ρ on a finite dimensional vector space V, all defined over the complex number field C.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

[ 1 ] Sato, M. and Kimura, T., A classification of irreducible prehomogeneous vector spaces and their invariants, Nagoya Math. J., 65 (1977), 1155.Google Scholar
[ 2 ] Sato, M. and Shintani, T., On zeta functions associated with prehomogeneous vector spaces, Ann. of Math., 100 (1974), 131170.Google Scholar
[ 3 ] Shintani, T., On zeta functions associated with the vector space of quadratic forms, J. Fac. Sci., Univ. Tokyo, 22 (1975), 2565.Google Scholar
[ 4 ] Sato, F., Zeta functions in several variables associated with prehomogeneous vector spaces I: Functional equations, Tôhoku Math. J., The second series, 34, no. 3, (1982), 453483.CrossRefGoogle Scholar
[ 5 ] Bernstein, I. N. and Gelfand, S. I., Meromorphic property of the functions Pλ , Funct. Anal. Appl., 3 (1969), 6869.CrossRefGoogle Scholar
[ 6 ] Teranishi, Y., Relative invariants and ò-functions of prehomogeneous vector spaces Nagoya Math. J., 98 (1985), 139156.Google Scholar
[ 7 ] Bruhat, F., Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France, 84 (1956), 97205.CrossRefGoogle Scholar