Semisimple orbital integrals on the symplectic space for a real reductive dual pair

M. Mckee (1) , A. Pasquale (2) , T. Przebinda (1)

1 OU - University of Oklahoma
2 IECL - Institut Élie Cartan de Lorraine

We prove a Weyl Harish-Chandra integration formula for the action of a reductive dual pair on the corresponding symplectic space W. As an intermediate step, we introduce a notion of a Cartan subspace and a notion of an almost semisimple element in the symplectic space W. We prove that the almost semisimple elements are dense in W. Finally, we provide estimates for the orbital integrals associated with the different Cartan subspaces in W.

Mots clés: Orbital integrals; Lie superalgebras; Reductive dual pairs

Domaines: Mathématiques [math]

M. Mckee, A. Pasquale, T. Przebinda. Semisimple orbital integrals on the symplectic space for a real reductive dual pair. Journal of Functional Analysis, 2015, 268 (2), pp.278-335. ⟨10.1016/j.jfa.2014.10.002⟩. ⟨hal-01096793⟩