%0 Journal Article
%T Semisimple orbital integrals on the symplectic space for a real reductive dual pair
%A M. McKee
%A A. Pasquale
%A T. Przebinda
%J Mathematics
%D 2011
%I arXiv
%X 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 $W$.
%U http://arxiv.org/abs/1112.0479v2