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

M. McKee; A. Pasquale; T. Przebinda

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arXiv · 1112.0479

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

M. McKee·A. Pasquale·T. Przebinda

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Abstract

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 $W$.

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BibTeX RIS

M. McKee, A. Pasquale, T. Przebinda. 2014-10-05. Semisimple orbital integrals on the symplectic space for a real reductive dual pair. https://arxiv.org/abs/1112.0479

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