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Sur la structure transverse à une orbite nilpotente adjointe

Published online by Cambridge University Press:  20 November 2018

Hervé Sabourin
Hervé Sabourin*
Affiliation:
UMR 6086 CNRS, Département de Mathématiques, Téléport 2, BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope-Chasseneuil Cedex, France, e-mail: sabourin@mathlabo.univ-poitiers.fr
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Abstract

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We are interested in Poisson structures transverse to nilpotent adjoint orbits in a complex semi-simple Lie algebra, and we study their polynomial nature. Furthermore, in the case of $s{{l}_{n}}$, we construct some families of nilpotent orbits with quadratic transverse structures.

Keywords

22E53Dnilpotent adjoint orbitsconormal orbitsPoisson transverse structure
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 4 , 01 August 2005 , pp. 750 - 770
Copyright
Copyright © Canadian Mathematical Society 2005

References

[BE-GO] Bergmann, P. G. et Goldberg, I., Dirac bracket transformations in phase space. Phys. Rev. 98(1955), 531–538.Google Scholar
[CU-RO] Cushman, R. et Roberts, M., Poisson structures transverse to coadjoint orbits. Bull. Sci. Math. 126(2002), 525–534.Google Scholar
[DA] Damianou, P. A., Transverse Poisson structures of coadjoint orbits. Bull. Sci. Math. 120(1996), 195–214.Google Scholar
[DI] Dixmier, J., Enveloping Algebras. Graduate Studies in Mathematics 11, American Mathematical Society, Providence, RI, 1996.Google Scholar
[OH] Oh, Y.-G., Some remarks on the transverse Poisson structures of coadjoint orbits. Lett. Math. Phys. 12(1986), 87–91.Google Scholar
[PA1] Panyushev, D., On spherical nilpotent orbits and beyond. Ann. Inst. Fourier (Grenoble) 49(1999), 1453–1476.Google Scholar
[PA2] Panyushev, D., Complexity and rank of actions in invariant theory. J. Math. Science (New York) 95(1999), 1925–1985.Google Scholar
[RA] Raïs, M., La représentation coadjointe du groupe affine. Ann. Inst. Fourier (Grenoble) 28(1978), 207–237.Google Scholar
[RO] Roberts, M., Wulff, C., et Lamb, J. S. W., Hamiltonian systems near relative equilibria. J. Differential Equations 179(2002), 562–604.Google Scholar
[SG] Saint-Germain, M., Poisson algebras and transverse structures. Geom, J.. Phys. 31(1999), 153–194.Google Scholar
[SL] Slodowy, P., Simple Singularities and Simple Algebraic Groups. Lecture Notes in Mathematics 815, Springer-Verlag, Berlin, 1980.Google Scholar
[SP-ST] Springer, T. A. et Steinberg, R., Conjugacy classes. Dans : Seminar on Algebraic Groups and Related Finite Groups, éd. Borel, A., et al., Lecture Notes in Mathematics 131, Springer, Berlin, 1970, pp. 167–266.Google Scholar
[WE] A.Weinstein, Local structure of Poisson manifolds. J. Differential Geom. 18(1986), 523–557.Google Scholar