English

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 WW. As an intermediate step, we introduce a notion of a Cartan subspace and a notion of an almost semisimple element in the symplectic space WW. We prove that the almost semisimple elements are dense in WW. Finally, we provide estimates for the orbital integrals associated with the different Cartan subspaces in WW.

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}
}