Derivatives of elliptic orbital integrals on a symplectic space

M. Mckee (1) , Angela Pasquale (2) , T. Przebinda (3)

1 McGill University = Université McGill [Montréal, Canada]
2 IECL - Institut Élie Cartan de Lorraine
3 Department of Mathematics [Norman]

For a real reductive dual pair with one member compact we study the orbital integrals on the corresponding symplectic space that occur in the Weyl-Harish-Chandra integration formula on that space. We obtain estimates of the derivatives of such integrals. These estimates are needed for expressing the intertwining distribution attached to a pair of representations in Howe's correspondence in terms of the orbital integrals. This is in analogy to Harish-Chandra's theory, where the distribution character of an irreducible admissible representation of a real reductive group factors through the semisimple orbital integrals on the group.

Mots clés: Reductive dual pairs; Howe duality; Weyl calculus; Lie superalgebras

Domaines: Mathématiques [math]

M. Mckee, Angela Pasquale, T. Przebinda. Derivatives of elliptic orbital integrals on a symplectic space. Journal of Lie Theory, 2020, 30 (2), pp.489-512. ⟨hal-02919139⟩