1. CJM 2005 (vol 57 pp. 750)
|Sur la structure transverse Ã une orbite nilpotente adjointe |
We are interested in Poisson structures to transverse nilpotent adjoint orbits in a complex semi-simple Lie algebra, and we study their polynomial nature. Furthermore, in the case of $sl_n$, we construct some families of nilpotent orbits with quadratic transverse structures.
Keywords:nilpotent adjoint orbits, conormal orbits, Poisson transverse structure
2. CJM 2000 (vol 52 pp. 897)
|Higher Order Scattering on Asymptotically Euclidean Manifolds |
We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time $\pi$ on the boundary. Furthermore, it is shown that on $\Real^n$ the asymptotics of certain short-range perturbations of $\Delta^k$ can be recovered from the scattering matrix at a finite number of energies.
Keywords:scattering theory, conormal, Lagrangian