Semisimple orbital integrals on the symplectic space for a real reductive dual pairReport as inadecuate




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1 Department of Mathematics 2 Analyse IECL - Institut Élie Cartan de Lorraine 3 Department of Mathematics

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.

Keywords : Lie superalgebras Reductive dual pairs Orbital integrals





Author: M. Mckee - A. Pasquale - T. Przebinda -

Source: https://hal.archives-ouvertes.fr/



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