The Fourier transform of semi-simple coadjoint orbits

Paul-Emile Paradan (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Let M be a closed coadjoint orbit of a real, connected, semi-simple Lie group G, and let F(M) be its Fourier transform. In this paper we compute the restriction of F(M) to the Lie algebra of a maximal compact subgroup K of G. Using our technique of localization in equivariant cohomology developed recently, we extend previous results by M. Duflo, G. Heckman, M. Vergne, and I. Sengupta.

Domaines: Géométrie symplectique [math.SG]

Paul-Emile Paradan. The Fourier transform of semi-simple coadjoint orbits. Journal of Functional Analysis, 1999, 163, pp.152-179. ⟨10.1006/jfan.1998.3381⟩. ⟨hal-00773249⟩