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The b-functions and holonomy diagrams of irreducible regular prehomogeneous vector spaces

Published online by Cambridge University Press:  22 January 2016

Tatsuo Kimura
Tatsuo Kimura*
Affiliation:
Institute of Mathematics, University of Tsukuba
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The purpose of this paper is to investigate the micro-local structure and to calculate, by constructing the holonomy diagrams, the b-functions (See [2]) of irreducible regular prehomogeneous vector spaces (See [1]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 85 , March 1982 , pp. 1 - 80
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[ 1 ] Sato, M and Kimura, T, A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J., 65 (1977), 1–155.CrossRefGoogle Scholar
[ 2 ] Sato, M. Kashiwara, M. Kimura, T. and Oshima, T, Micro-local analysis of prehomogeneous vector spaces, Inv. math., 62 (1980), 117–179.CrossRefGoogle Scholar
[ 3 ] Igusa, J-I., A classification of spinors up to dimension twelve, Amer. J. of Math., 92, No. 4 (1970), 997–1028.CrossRefGoogle Scholar
[ 4 ] Chevalley, C, The Algebraic Theory of Spinors, Columbia University Press, 1954.CrossRefGoogle Scholar
[ 5 ] Haris, S.J., Some irreducible representation of exceptional algebraic groups, Amer. J. of Math., 93 (1971).CrossRefGoogle Scholar
[ 6 ] Gurevich, G.B., Foundations of the Theory of Algebraic Invariants, P. Noordhoff LTD-Groningen, 1964.Google Scholar
[ 7 ] Kimura, T, Study of irreducible prehomogeneous vector spaces, Master Thesis in Japanese, University of Tokyo, 1973, 373 pp.Google Scholar
[ 8 ] Kawahara, H, Prehomogeneous vector spaces related with the spin group, Master Thesis in Japanese, University of Tokyo, 1974.Google Scholar
[ 9 ] Popov, V.L., A classification of spinors of dimension fourteen, Uspechi Math. Nauk, 32, (1977).Google Scholar
[10] Gatti, V and Viniberghi, E, Spinors of 13-dimensional space, Adv. Math., 30, No. 2 (1978).CrossRefGoogle Scholar
[11] Ozeki, I, On the micro-local structure of the regular prehomogeneous vector space associated with SL(5) X GL(4), I, Proc. Japan Acad., 55, Ser. A, (1979).CrossRefGoogle Scholar
[12] Kimura, T and Muro, M, On some series of regular irreducible prehomogeneous vector spaces, Proc. Japan Acad., 55, Ser A, No. 10 (1979), 384–389.Google Scholar
[13] Ozeki, I., On the micro-local structure of a regular prehomogeneous vector space associated with GL(8), Proc. Japan Acad., 56, Ser. A, No. 1 (1980), 18–21.Google Scholar
[14] Kimura, T., Remark on some combinatorial construction of relative invariants, Tsukuba J. of Math., 5, No. 1 (1981).CrossRefGoogle Scholar
[15] Kimura, T. and Ozeki, I., On the micro-local structure of regular prehomogenous vector space associated with Spin (10) X GL(3). (in preparation).Google Scholar