Semisimple orbital integrals on the symplectic space for a real reductive dual pair
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 $W$.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2011
- DOI:
- 10.48550/arXiv.1112.0479
- arXiv:
- arXiv:1112.0479
- Bibcode:
- 2011arXiv1112.0479M
- Keywords:
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- Mathematics - Representation Theory
- E-Print:
- J. Funct. Anal. 268 (2015), 278-335