Semisimple orbital integrals on the symplectic space for a real reductive dual pair
Representation Theory
2015-11-16 v2
Abstract
We prove a Weyl Harish-Chandra integration formula for the action of a reductive dual pair on the corresponding symplectic space . As an intermediate step, we introduce a notion of a Cartan subspace and a notion of an almost semisimple element in the symplectic space . We prove that the almost semisimple elements are dense in . Finally, we provide estimates for the orbital integrals associated with the different Cartan subspaces in .
Keywords
Cite
@article{arxiv.1112.0479,
title = {Semisimple orbital integrals on the symplectic space for a real reductive dual pair},
author = {M. McKee and A. Pasquale and T. Przebinda},
journal= {arXiv preprint arXiv:1112.0479},
year = {2015}
}