Geodesic
Sur la structure transverse à une orbite nilpotente adjointe
Canadian journal of mathematics, Tome 57 (2005) no. 4, pp. 750-770

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2005-030-4
Mots-clés : 22E, 53D, nilpotent adjoint orbits, conormal orbits, Poisson transverse structure 
Sabourin, Hervé. Sur la structure transverse à une orbite nilpotente adjointe. Canadian journal of mathematics, Tome 57 (2005) no. 4, pp. 750-770. doi: 10.4153/CJM-2005-030-4
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[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

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