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Z-graduations de type parabolique et polynomes harmoniques

Published online by Cambridge University Press:  22 January 2016

Abdel Latif Mortajine
Abdel Latif Mortajine*
Affiliation:
Département de Mathématiques-URA 750 CNRS, Université de Nancy, 1, BP 239, 54506 Vandoeuvre les Nancy Cedex, mortajin@iecn.u-nancy.fr
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Abstract

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We give pluriharmonic and harmonic representations of prehomogeneous vector spaces of regular classical parabolic type (L = Γ×M, V) througt the commutative quotients V ‖ M = spec(C[V]M) of them.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 153 , 1999 , pp. 31 - 51
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

References

Bibliographie

[Bo] Bourbaki, N., Algébre de Lie, chap. 7–8, Hermann.Google Scholar
[Ko-Sah] Kostant, B. and Sahi, S., The Capelli identity, tube domains and the generalized laplace transform, Adv. in Math., 87 (1991), 71–92.Google Scholar
[Ho] Howe, R., Perspectives in invariant theory, I. M. C. P., 8 (1995), 1–182.Google Scholar
[Ka] Kac, V. G., Some remarks on nilpotent orbits, J.Algebras, 64 (1980).Google Scholar
[Ho-Um] How, R. and Umeda, T., The Capelli identity, the double theorem, and multiplicity-free actions, Math. Ann., 290 (1991).Google Scholar
[K-V] Kashiwara, M. and Vergne, M., On the Segal-Shale-Weil representation and harmonic polynomials, Inv. Math., 44 (1978), 1–47.Google Scholar
[Lu] Luna, D., Slices etales, Bull. Cos. Math. France Mémoire, 33 (1973), 81–105.Google Scholar
[Mor 1] Mortajine, A. L., Classification des espaces préhomogénes de type parabolique réguliers et de leurs invariants relatifs, Travaux en cours, 40 (1991).Google Scholar
[Mor 2] Mortajine, A. L., Z-graduation de type parabolique et théorie des invariants, Prépublication de l’IECN 1/97 (1997).Google Scholar
[Mu-Ru-Sch] Muller, I., Rubenthaler, H. and Schiffmann, G., Structure des espaces préhomogénes associés á certaines algèbres de Lie graduées, Math. Ann., 274 (1986).Google Scholar
[Mum] Mumford, D., Geometric invariant theory, Academic Press, New York, 1965.Google Scholar
[Po] Popov, V., Groups, generators, syzygies, and orbits in invariant theory, Transl. Mono., 100, American Math. Coc., Providence, R. I., 145–156.Google Scholar
[Ru] Rubenthaler, H., Espaces préhomogènes de type parabolique, thèse d’Etat,, IRMA (1982).Google Scholar
[Ru-Sch] Rubenthaler, H. and Schiffmann, G., Opérateurs différentiels de Shimura et espaces préhomogènes, Inv. Math., 90 (1987), 409–488.Google Scholar
[Sa III] Sato, F., Zeta function associated with puch mogenaous vector spaces III: Einsenstein series of indefinite quadratic forms, Ann. Math., 116 (1982).Google Scholar
[Sa I] Sato, F., Zeta function of several variables associated with prehomogeneous vector spaces I: functional equation, Tohoko Math. Japan, 34 (1982), 437–483.Google Scholar
[FS] Sato, F., Zeta function with polynomial coefficients associated with prehomogeneous vector spaces, Preprint.Google Scholar
[S-K] Sato, and Kimura, T., Classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J., 65 (1877).Google Scholar
[Shim] Shimura, G., On differential operators attached to certain representations of classical groups, Inv. Math., 77 (1984), 463–442.Google Scholar
[Sp] Springer, , Invariant theory, L. N. M., 585, 1977.Google Scholar
[Sr] Servidio, F., Prehomogeneous spaces and varieties, TAMS, 76 (1973), 421–444.Google Scholar
[V] Vinberg, E. B., On the classification of the nilpotent elements of graded Lie algebras, Soviet Math. Dokl., 16 (1975), 1517–1520.Google Scholar
[V-K] Vinberg, E. B. and Kimelfeld, , Homogeneous domains in flag manifolds and spherical subgroups of semi-simple Lie groups, Func. Anal. Appli., 12 (1978), 12–19.Google Scholar
[W] Weyl, A., The classical groups, Princeton University Press, Princeton, N. J., 1946.Google Scholar